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Chapter 13: Problem 43

Verify, using the ideal gas law, the assertion in Problem 38 that 1.00 mol of a gas at \(0.0^{\circ} \mathrm{C}\) and 1.00 atm occupies a volume of $0.0224 \mathrm{m}^{3}$

Short Answer

Expert verified
Question: Verify the following assertion using the ideal gas law: 1.00 mole of an ideal gas at 0.0 掳C and a pressure of 1.00 atmosphere occupies a volume of 0.0224 m鲁. Answer: The assertion is verified using the ideal gas law. The calculated volume of the gas is 0.0224 m鲁, which matches the given assertion.

Step by step solution

01

Convert the temperature to Kelvin

Convert the given temperature in Celsius to Kelvin: T(K) = T(掳C) + 273.15, where T(K) is the temperature in Kelvin and T(掳C) is the temperature in Celsius. T(K) = 0.0 + 273.15 = 273.15 K
02

Convert the pressure to Pascals

Convert the given pressure in atmospheres to Pascals: P(Pa) = P(atm) * 101325, where P(Pa) is the pressure in Pascals and P(atm) is the pressure in atmospheres. P(Pa) = 1.00 * 101325 = 101325 Pa
03

Substitute the values into the ideal gas law equation

Substitute the given values and the converted values of temperature and pressure in the ideal gas law equation: PV = nRT (101325 Pa)(V) = (1.00 mol)(8.314 J/(mol路K))(273.15 K)
04

Solve for the volume of the gas

Solve the equation for volume (V) by dividing both sides by 101325 Pa: V = (1.00 mol)(8.314 J/(mol路K))(273.15 K) / 101325 Pa = 0.0224 m鲁 The calculated volume of the gas is 0.0224 m鲁, which matches the assertion given in the problem. Therefore, the assertion is verified using the ideal gas law.

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