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A given simple of an ideal gas occupies a volume V at a pressure P and absolute temperature T . The mass of each molecule of the gas is m. Which of the following gives the density of the gas ? A. P/kT B. Pm/kT C. P/kTV D. mkT?
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Answer:
Introduction:
The given problem asks to determine the density of an ideal gas. The density of a gas is defined as the mass of the gas per unit volume. In order to find the density, we need to consider the given parameters: volume (V), pressure (P), absolute temperature (T), and mass of each molecule (m).
Density formula:
The density of a gas can be calculated using the formula:
Density (ρ) = mass (m) / volume (V)
Deriving the density formula:
To derive the formula for density, we need to consider the ideal gas law and the definition of density. The ideal gas law states that:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant
T = absolute temperature
The number of moles (n) can be calculated using the formula:
n = mass (m) / molar mass (M)
Where:
m = mass of gas
M = molar mass of gas
Substituting this value into the ideal gas law equation:
PV = (m/M)RT
We can rearrange this equation to solve for the mass:
m = (PV)(M) / RT
Calculating density:
Now that we have an expression for the mass (m), we can substitute it into the density formula:
ρ = m / V
Substituting the expression for mass:
ρ = [(PV)(M) / RT] / V
Simplifying the expression:
ρ = P(M) / (RT)
Final answer:
Therefore, the density of the gas is given by:
ρ = P(M) / (RT)
Explanation:
The correct answer is option B: Pm/kT. This is because the density formula derived above matches the expression Pm/kT. Option A (P/kT), option C (P/kTV), and option D (mkT) do not correctly represent the density formula.
Introduction:
The given problem asks to determine the density of an ideal gas. The density of a gas is defined as the mass of the gas per unit volume. In order to find the density, we need to consider the given parameters: volume (V), pressure (P), absolute temperature (T), and mass of each molecule (m).
Density formula:
The density of a gas can be calculated using the formula:
Density (ρ) = mass (m) / volume (V)
Deriving the density formula:
To derive the formula for density, we need to consider the ideal gas law and the definition of density. The ideal gas law states that:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant
T = absolute temperature
The number of moles (n) can be calculated using the formula:
n = mass (m) / molar mass (M)
Where:
m = mass of gas
M = molar mass of gas
Substituting this value into the ideal gas law equation:
PV = (m/M)RT
We can rearrange this equation to solve for the mass:
m = (PV)(M) / RT
Calculating density:
Now that we have an expression for the mass (m), we can substitute it into the density formula:
ρ = m / V
Substituting the expression for mass:
ρ = [(PV)(M) / RT] / V
Simplifying the expression:
ρ = P(M) / (RT)
Final answer:
Therefore, the density of the gas is given by:
ρ = P(M) / (RT)
Explanation:
The correct answer is option B: Pm/kT. This is because the density formula derived above matches the expression Pm/kT. Option A (P/kT), option C (P/kTV), and option D (mkT) do not correctly represent the density formula.
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A given simple of an ideal gas occupies a volume V at a pressure P and absolute temperature T . The mass of each molecule of the gas is m. Which of the following gives the density of the gas ? A. P/kT B. Pm/kT C. P/kTV D. mkT?
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A given simple of an ideal gas occupies a volume V at a pressure P and absolute temperature T . The mass of each molecule of the gas is m. Which of the following gives the density of the gas ? A. P/kT B. Pm/kT C. P/kTV D. mkT? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A given simple of an ideal gas occupies a volume V at a pressure P and absolute temperature T . The mass of each molecule of the gas is m. Which of the following gives the density of the gas ? A. P/kT B. Pm/kT C. P/kTV D. mkT? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A given simple of an ideal gas occupies a volume V at a pressure P and absolute temperature T . The mass of each molecule of the gas is m. Which of the following gives the density of the gas ? A. P/kT B. Pm/kT C. P/kTV D. mkT?.
A given simple of an ideal gas occupies a volume V at a pressure P and absolute temperature T . The mass of each molecule of the gas is m. Which of the following gives the density of the gas ? A. P/kT B. Pm/kT C. P/kTV D. mkT? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A given simple of an ideal gas occupies a volume V at a pressure P and absolute temperature T . The mass of each molecule of the gas is m. Which of the following gives the density of the gas ? A. P/kT B. Pm/kT C. P/kTV D. mkT? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A given simple of an ideal gas occupies a volume V at a pressure P and absolute temperature T . The mass of each molecule of the gas is m. Which of the following gives the density of the gas ? A. P/kT B. Pm/kT C. P/kTV D. mkT?.
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