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Parts-per notation is a set of pseudo-units used in science and engineering to describe small values of dimensionless quantities like mole fraction or mass fraction, and these notations are considered pure numbers because their units of measurement always cancel out.
Answer: True
Explanation: Parts-per notation serves as pseudo-units for dimensionless quantities, and their units cancel out, rendering them pure numbers.
One part per hundred is commonly represented by the percent sign (%) and has a value of 10⁻², equivalent to about fourteen minutes out of one day.
Answer: True
Explanation: The percent sign (%) represents one part per hundred (10⁻²), which is approximately fourteen minutes out of one day.
One part per ten thousand is denoted by the permyriad sign (‱) and is equivalent to about nine seconds out of one day.
Answer: True
Explanation: The permyriad sign (‱) denotes one part per ten thousand (10⁻⁴), which is equivalent to approximately nine seconds out of one day.
Parts-per notations are considered 'pure numbers' because they are quantity-per-quantity measures where units of measurement always cancel out.
Answer: True
Explanation: Parts-per notations are dimensionless 'pure numbers' because they represent ratios of quantities of the same measure, causing their units to cancel out.
The four commonly used parts-per notations are ppm, ppb, ppt, and ppq, representing 10⁻⁶, 10⁻⁹, 10⁻¹², and 10⁻¹⁵ respectively.
Answer: True
Explanation: The four commonly used parts-per notations are indeed ppm (10⁻⁶), ppb (10⁻⁹), ppt (10⁻¹²), and ppq (10⁻¹⁵).
Parts-per notation can only be expressed using specific, predefined units of measure, and changing the units would alter its numeric value.
Answer: False
Explanation: Parts-per notations represent relative proportions and can be expressed using any units of the same measure (e.g., µm/m or µ in/in) without altering their numeric value.
One part per thousand has a value of 10⁻³ and is equivalent to about ninety seconds out of one day.
Answer: True
Explanation: One part per thousand (‰) has a value of 10⁻³ and is equivalent to approximately ninety seconds out of one day.
What is the primary characteristic of parts-per notation in science and engineering?
Answer: It describes small values of dimensionless quantities as pseudo-units.
Explanation: Parts-per notation is characterized as a set of pseudo-units used to describe small values of dimensionless quantities in science and engineering.
Why are parts-per notations considered 'pure numbers' without associated units of measurement?
Answer: They are quantity-per-quantity measures where units of measurement always cancel out.
Explanation: Parts-per notations are dimensionless 'pure numbers' because they are derived from quantity-per-quantity measures, ensuring that their units of measurement always cancel out.
Which of the following is NOT one of the four commonly used parts-per notations mentioned in the text?
Answer: Parts-per-quintillion (ppq)
Explanation: The text identifies parts-per-million (ppm), parts-per-billion (ppb), parts-per-trillion (ppt), and parts-per-quadrillion (ppq) as the four commonly used parts-per notations. However, it also notes that measurements at the ppq level are 'relatively uncommon' in analytical chemistry.
What is the common representation and value of 'one part per hundred'?
Answer: Percent sign (%), 10⁻²
Explanation: One part per hundred is commonly represented by the percent sign (%) and has a value of 10⁻².
What is the time equivalent for 'one part per ten thousand'?
Answer: About nine seconds out of one day.
Explanation: One part per ten thousand (‱) is equivalent to approximately nine seconds out of one day.
In chemistry, particularly for dilute aqueous solutions, 1 ppm is commonly equated to 1 mg/L, assuming the density of water is 1.00 g/mL.
Answer: True
Explanation: For dilute aqueous solutions, assuming water density of 1.00 g/mL, 1 ppm is equivalent to 1 mg/L, and 1 ppb to 1 µg/L.
Parts-per notation is exclusively used in chemistry for dilute solutions and is not applied in physics or engineering to express proportional phenomena.
Answer: False
Explanation: Parts-per notation is widely used in physics and engineering to express proportional phenomena, changes, stability, and uncertainty in measurements, not exclusively in chemistry.
As fluorescein aqueous solutions are diluted from 10,000 ppm to 1 ppm, their color transitions from deep red to orange, then vibrant yellow, and finally a very pale yellow.
Answer: True
Explanation: The color of fluorescein aqueous solutions changes distinctly with dilution, progressing from deep red at 10,000 ppm through orange and vibrant yellow to a very pale yellow at 1 ppm.
In nuclear magnetic resonance spectroscopy (NMR), chemical shift is expressed in ppm to ensure the quantity depends directly on the instrument's magnetic field strength.
Answer: False
Explanation: In NMR, chemical shift is expressed in ppm to provide a dimensionless quantity that is independent of the instrument's magnetic field strength, not dependent on it.
Per cent mille (pcm) denotes one part per 10,000 parts and is primarily used in financial contexts to denote changes in interest rates.
Answer: False
Explanation: Per cent mille (pcm) denotes one part per 100,000 (10⁻⁵) parts and is primarily used in epidemiology and nuclear reactor engineering, not financial contexts for interest rates (which use basis points, 10⁻⁴).
One part per million (ppm) is equivalent to approximately 32 seconds out of a year and 1 mm of error per kilometer of distance traversed.
Answer: True
Explanation: One part per million (ppm) is indeed equivalent to approximately 32 seconds out of a year and 1 mm of error per kilometer of distance traversed.
Parts per billion (ppb) represents one part per 10⁶ parts, equivalent to approximately three seconds out of a century.
Answer: False
Explanation: Parts per billion (ppb) represents one part per 10⁹ parts, not 10⁶, and is equivalent to approximately three seconds out of a century.
Measurements at the parts-per-quadrillion (ppq) level are never performed in analytical chemistry due to their extreme difficulty.
Answer: False
Explanation: Measurements at the parts-per-quadrillion (ppq) level are indeed performed in analytical chemistry, despite their difficulty, as exemplified by EPA limits for dioxin.
A laser rangefinder's accuracy of '±(1 mm + 1 ppm)' implies that the measurement error is solely a fixed component of 1 mm, with no proportional error.
Answer: False
Explanation: A laser rangefinder's accuracy of '±(1 mm + 1 ppm)' signifies that the measurement error comprises both a fixed component (1 mm) and a proportional component (1 ppm), meaning the error increases with distance.
In finance, a basis point represents one hundredth of a percent, which is equivalent to one part per million.
Answer: False
Explanation: In finance, a basis point represents one hundredth of a percent, which is equivalent to one part per ten thousand (10⁻⁴), not one part per million (10⁻⁶).
One pcm (per cent mille) is equivalent to about 5 minutes out of a year in time measurement and 1 cm of error per kilometer in distance measurement.
Answer: True
Explanation: One pcm (per cent mille) is equivalent to approximately 5 minutes out of a year and 1 cm of error per kilometer, as stated.
Parts per trillion (ppt) denotes one part per 10¹⁵ parts, equivalent to about thirty seconds out of every million years.
Answer: False
Explanation: Parts per trillion (ppt) denotes one part per 10¹² parts, not 10¹⁵, and is equivalent to about thirty seconds out of every million years.
Parts per quadrillion (ppq) denotes one part per 10¹⁵ parts, equivalent to approximately two and a half minutes out of the age of the Earth.
Answer: True
Explanation: Parts per quadrillion (ppq) denotes one part per 10¹⁵ parts and is equivalent to approximately two and a half minutes out of the age of the Earth.
The U.S. Environmental Protection Agency (EPA) sets a hard limit of 30 ppb for dioxin in drinking water.
Answer: False
Explanation: The U.S. Environmental Protection Agency (EPA) sets a hard limit of 30 ppq for dioxin in drinking water, not 30 ppb.
In chemistry, when describing dilute aqueous solutions, what common equivalence is made for 1 ppm?
Answer: 1 mg/L, assuming water density is 1.00 g/mL.
Explanation: For dilute aqueous solutions, assuming a water density of 1.00 g/mL, 1 ppm is commonly equated to 1 mg/L.
How is parts-per notation used in physics and engineering beyond expressing proportional phenomena?
Answer: To denote the change, stability, or uncertainty in measurements.
Explanation: In physics and engineering, parts-per notation is also used to express the change, stability, or uncertainty inherent in various measurements.
What color is a fluorescein aqueous solution at a concentration of 10,000 ppm?
Answer: Deep red
Explanation: At a concentration of 10,000 ppm, a fluorescein aqueous solution exhibits a deep red color.
In nuclear magnetic resonance spectroscopy (NMR), why is chemical shift usually expressed in ppm?
Answer: To ensure it is a dimensionless quantity independent of magnetic field strength.
Explanation: Chemical shift in NMR is expressed in ppm to render it a dimensionless quantity, thereby making it independent of the instrument's magnetic field strength.
In finance, what does a basis point typically denote?
Answer: Changes in or differences between percentage interest rates, equivalent to one part per ten thousand.
Explanation: In finance, a basis point denotes changes in or differences between percentage interest rates, equivalent to one part per ten thousand (10⁻⁴).
What is 'per cent mille' (pcm) commonly used for?
Answer: Epidemiology for mortality, crime, and disease prevalence rates, and nuclear reactor engineering.
Explanation: Per cent mille (pcm) is commonly used in epidemiology for rates of mortality, crime, and disease prevalence, as well as in nuclear reactor engineering for reactivity.
What is the time equivalent for 'one part per hundred thousand' (pcm) out of a year?
Answer: About 5 minutes.
Explanation: One part per hundred thousand (pcm) is equivalent to approximately 5 minutes out of a year.
What is the equivalent of one part per million (ppm) in mining?
Answer: One gram per metric ton (g/t)
Explanation: In mining, one part per million (ppm) is equivalent to one gram per metric ton (g/t).
What is the time equivalent for 'parts per billion' (ppb)?
Answer: Approximately three seconds out of a century.
Explanation: Parts per billion (ppb) is equivalent to approximately three seconds out of a century.
What is the time equivalent for 'parts per trillion' (ppt)?
Answer: About thirty seconds out of every million years.
Explanation: Parts per trillion (ppt) is equivalent to approximately thirty seconds out of every million years.
What is the U.S. Environmental Protection Agency (EPA) hard limit for dioxin in drinking water?
Answer: 30 ppq
Explanation: The U.S. Environmental Protection Agency (EPA) sets a hard limit of 30 ppq for dioxin in drinking water.
How does a laser rangefinder's accuracy specification of '±(1 mm + 1 ppm)' illustrate the use of ppm?
Answer: It demonstrates that the measurement error includes both a fixed and a proportional component.
Explanation: The accuracy specification '±(1 mm + 1 ppm)' for a laser rangefinder illustrates that the total measurement error comprises both a fixed component (1 mm) and a component proportional to the measured distance (1 ppm).
The abbreviation 'ppt' is universally understood to mean 'parts per thousand' and is recommended for expressing this quantity to avoid confusion.
Answer: False
Explanation: The abbreviation 'ppt' is ambiguous, commonly meaning 'parts per trillion' but sometimes 'parts per thousand', leading to confusion. It is generally recommended to avoid 'ppt' for 'parts per thousand'.
A significant problem with parts-per notation is that it often fails to specify whether it refers to mass fraction, mole fraction, or volume fraction, especially with gases.
Answer: True
Explanation: A significant problem with parts-per notation is its common failure to specify the type of fraction (mass, mole, or volume), which can lead to misinterpretation, particularly for gases.
When using parts-per notation for gases, specifying the type of fraction (mass, mole, or volume) is unimportant because the conversion factors are negligible.
Answer: False
Explanation: For gases, specifying the type of fraction (mass, mole, or volume) is crucial because the conversion factors between these fractions can be quite significant, not negligible.
The suffix 'V' or 'v' is sometimes appended to parts-per notation (e.g., ppmV) to indicate that the measurement refers to volume fraction.
Answer: True
Explanation: The suffix 'V' or 'v' is indeed appended to parts-per notation (e.g., ppmV) to clarify that the measurement pertains to volume fraction.
The literal interpretation of 'volume fraction' (what volume of a pure substance is in a given volume of mixture) is commonly used with 'ppbv' and 'pptv'.
Answer: False
Explanation: While 'ppbv' and 'pptv' are typically used to denote mole fractions, the literal interpretation of 'volume fraction' is rarely applied, except in specific cases like alcohol by volume.
To distinguish mass fraction from volume or mole fraction, the letter 'w' is sometimes added to the abbreviation, such as ppmw or ppbw.
Answer: True
Explanation: The letter 'w' (for 'weight') is sometimes added to parts-per abbreviations (e.g., ppmw, ppbw) to specifically indicate mass fraction, differentiating it from volume or mole fraction.
The inconsistent usage of parts-per notation across scientific disciplines rarely causes problems, as researchers typically understand the context-specific meanings.
Answer: False
Explanation: The inconsistent usage of parts-per notation across scientific disciplines frequently causes problems, leading to misinterpretation, especially by non-experts, due to a failure to specify details in publications.
Why is the abbreviation 'ppt' generally avoided for 'one part per thousand'?
Answer: It is usually understood to represent 'parts per trillion'.
Explanation: The abbreviation 'ppt' is generally avoided for 'one part per thousand' because it is more commonly understood to mean 'parts per trillion', leading to ambiguity.
What ambiguity exists with the abbreviation 'ppt'?
Answer: It usually means 'parts per trillion' but occasionally means 'parts per thousand'.
Explanation: The abbreviation 'ppt' is ambiguous because it commonly refers to 'parts per trillion' but can also mean 'parts per thousand', requiring contextual interpretation.
Why is it important to specify the type of fraction (mass, mole, or volume) when using parts-per notation, especially with gases?
Answer: The conversion factor between different fractions can be quite significant.
Explanation: Specifying the type of fraction (mass, mole, or volume) is critical for gases because the conversion factors between these different fractions can be highly significant, impacting measurement accuracy.
What suffixes are sometimes appended to parts-per notation to indicate volume fraction?
Answer: 'V' or 'v' (e.g., ppmV)
Explanation: The suffixes 'V' or 'v' are sometimes appended to parts-per notation (e.g., ppmV) to explicitly denote volume fraction.
How can mass fraction be distinguished from volume or mole fraction using parts-per notation?
Answer: By adding the letter 'w' (for 'weight') to the abbreviation.
Explanation: To differentiate mass fraction from volume or mole fraction, the letter 'w' (for 'weight') is sometimes added to the parts-per abbreviation, such as ppmw or ppbw.
The International System of Units (SI) formally recognizes parts-per notation as a standard unit of measurement, encouraging its use for clarity in scientific contexts.
Answer: False
Explanation: The International System of Units (SI) does not formally recognize parts-per notation, and its use can lead to ambiguity.
The International Bureau of Weights and Measures (BIPM) and the International Organization for Standardization (ISO) both formally recognize the percent symbol (%) as an official SI unit.
Answer: False
Explanation: Both BIPM and ISO state that the percent symbol (%) is not formally part of the SI, though it may be used with SI to represent 0.01 for dimensionless quantities.
The International Union of Pure and Applied Physics (IUPAP) considers the continued use of percent, ppm, ppb, and ppt a 'continued source of annoyance' for unit purists.
Answer: True
Explanation: The IUPAP indeed views the continued use of percent, ppm, ppb, and ppt as a 'continued source of annoyance' for unit purists, advocating for SI-compliant expressions.
The issue with 'long and short scales' in parts-per notation refers to the varying lengths of measurement instruments, which can lead to misinterpretation.
Answer: False
Explanation: The 'long and short scales' issue refers to the differing values of named numbers like 'billion' in various countries, leading to potential misunderstanding, not varying lengths of measurement instruments.
The U.S. National Institute of Standards and Technology (NIST) accepts the use of 'ppb' and 'ppt' with the SI, provided their definitions are clearly stated.
Answer: False
Explanation: The U.S. NIST takes a stringent position, stating that 'ppb' and 'ppt' are not acceptable for use with the SI due to their potential for ambiguity, even if defined.
The 'uno' (symbol: U) was a special name proposed by the International Union of Pure and Applied Physics (IUPAP) in 1999 to represent the number 1 in dimensionless quantities.
Answer: True
Explanation: The 'uno' (symbol: U) was indeed proposed by IUPAP in 1999 to represent the number 1 in dimensionless quantities, aiming to simplify SI expressions.
The 'uno' unit was widely adopted by standards organizations after its proposal in 1999 due to strong positive feedback.
Answer: False
Explanation: The 'uno' unit was not adopted by any standards organization; the response to its proposal was 'almost entirely negative'.
The red exclamation mark next to some parts-per abbreviations in the SI-compliant expressions table signifies that the BIPM explicitly does not recognize these abbreviations for dimensionless quantities within the SI.
Answer: True
Explanation: The red exclamation mark indicates that the BIPM explicitly does not recognize certain parts-per abbreviations (e.g., ‰, ‱, ppb, ppt, ppq) for dimensionless quantities within the SI.
The primary criticism of parts-per notation from international standards organizations is its lack of visual representation, making it hard to understand.
Answer: False
Explanation: The primary criticism from international standards organizations is that parts-per notation is not formally part of the SI and its meaning is ambiguous, not its lack of visual representation.
What is the official stance of the International System of Units (SI) regarding parts-per notation?
Answer: It is not formally part of the SI system and its meaning can be ambiguous.
Explanation: The International System of Units (SI) does not formally recognize parts-per notation, and its meaning is considered ambiguous, leading to potential misunderstandings.
What is the primary criticism from international standards organizations regarding parts-per notation?
Answer: It is not formally part of the SI and its meaning is ambiguous.
Explanation: International standards organizations primarily criticize parts-per notation because it is not formally part of the SI and its meaning can be ambiguous, leading to misinterpretation.
What is the stance of the International Bureau of Weights and Measures (BIPM) and the International Organization for Standardization (ISO) on the use of the percent symbol (%)?
Answer: It is not formally part of the SI, but may be used with the SI to represent 0.01 for dimensionless quantities.
Explanation: BIPM and ISO state that the percent symbol (%) is not formally part of the SI, but its use is permissible with the SI to represent 0.01 for dimensionless quantities.
According to the International Union of Pure and Applied Physics (IUPAP), what has been a 'continued source of annoyance' for unit purists?
Answer: The continued use of percent, ppm, ppb, and ppt.
Explanation: The IUPAP considers the continued use of percent, ppm, ppb, and ppt as a 'continued source of annoyance' for unit purists, who advocate for SI-compliant expressions.
What is the U.S. National Institute of Standards and Technology's (NIST) position on using 'ppb' and 'ppt' with the SI?
Answer: They are not acceptable for use with the SI due to potential for ambiguity.
Explanation: The U.S. NIST states that 'ppb' and 'ppt' are not acceptable for use with the SI due to their language-dependent nature and potential for ambiguity.
What does the red exclamation mark next to certain parts-per abbreviations in the SI-compliant expressions table signify?
Answer: It means the BIPM explicitly does not recognize these abbreviations for dimensionless quantities within the SI.
Explanation: The red exclamation mark signifies that the BIPM explicitly does not recognize the associated parts-per abbreviations as suitable for denoting dimensionless quantities within the SI.
SI-compliant units used as alternatives to parts-per notation are generally dimensionless quantities, where units of measurement factor out.
Answer: True
Explanation: SI-compliant alternatives for parts-per notation are indeed generally dimensionless quantities, where the units of measurement cancel out, resulting in pure-number coefficients.
An SI unit alternative for a mass fraction of '2 parts per million' would be 2 g/kg.
Answer: False
Explanation: An SI unit alternative for a mass fraction of '2 parts per million' would be 2 mg/kg, as 1 ppm is 1 part in 10⁶, and 1 mg/kg is 1 part in 10⁶.
An SI unit alternative for a stability of '1 part per million per minute' would be 1 (µA/A)/min.
Answer: True
Explanation: An SI unit alternative for a stability of '1 part per million per minute' is indeed 1 (µA/A)/min.
What is a general characteristic of SI-compliant units used as alternatives to parts-per notation?
Answer: They are, for the most part, dimensionless quantities where units factor out.
Explanation: SI-compliant units used as alternatives to parts-per notation are generally dimensionless quantities, where the units of measurement factor out, resulting in pure-number coefficients.
What SI unit would be an alternative for a strain of '2 parts per hundred'?
Answer: 2 cm/m
Explanation: An SI unit alternative for a strain of '2 parts per hundred' is 2 cm/m, representing a ratio of length to length.
What SI unit would be an alternative for a sensitivity of '2 parts per million'?
Answer: 2 µV/V
Explanation: An SI unit alternative for a sensitivity of '2 parts per million' is 2 µV/V, representing a ratio of microvolts to volts.
What SI unit would be an alternative for a mass fraction of '2 parts per million'?
Answer: 2 mg/kg
Explanation: An SI unit alternative for a mass fraction of '2 parts per million' is 2 mg/kg.
What SI unit would be an alternative for a mole fraction of '5.24 parts per million'?
Answer: 5.24 µmol/mol
Explanation: An SI unit alternative for a mole fraction of '5.24 parts per million' is 5.24 µmol/mol.
What SI unit would be an alternative for a temperature coefficient of '0.3 part per million per °C'?
Answer: 0.3 (µHz/Hz)/°C
Explanation: An SI unit alternative for a temperature coefficient of '0.3 part per million per °C' is 0.3 (µHz/Hz)/°C.