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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 °C and a pressure of 1.00 atmosphere occupies a volume of 0.0224 m³. Answer: The assertion is verified using the ideal gas law. The calculated volume of the gas is 0.0224 m³, 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(°C) + 273.15, where T(K) is the temperature in Kelvin and T(°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·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·K))(273.15 K) / 101325 Pa = 0.0224 m³ The calculated volume of the gas is 0.0224 m³, which matches the assertion given in the problem. Therefore, the assertion is verified using the ideal gas law.

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Most popular questions from this chapter

A cylindrical brass container with a base of \(75.0 \mathrm{cm}^{2}\) and height of \(20.0 \mathrm{cm}\) is filled to the brim with water when the system is at \(25.0^{\circ} \mathrm{C} .\) How much water overflows when the temperature of the water and the container is raised to \(95.0^{\circ} \mathrm{C} ?\)
A flat square of side \(s_{0}\) at temperature \(T_{0}\) expands by \(\Delta s\) in both length and width when the temperature increases by \(\Delta T\). The original area is \(s_{0}^{2}=A_{0}\) and the final area is $\left(s_{0}+\Delta s\right)^{2}=A .\( Show that if \)\Delta s \ll s_{0}$$$\frac{\Delta A}{A_{0}}=2 \alpha \Delta T$$(Although we derive this relation for a square plate, it applies to a flat area of any shape.)
A cylinder with an interior cross-sectional area of \(70.0 \mathrm{cm}^{2}\) has a moveable piston of mass \(5.40 \mathrm{kg}\) at the top that can move up and down without friction. The cylinder contains $2.25 \times 10^{-3} \mathrm{mol}\( of an ideal gas at \)23.0^{\circ} \mathrm{C} .$ (a) What is the volume of the gas when the piston is in equilibrium? Assume the air pressure outside the cylinder is 1.00 atm. (b) By what factor does the volume change if the gas temperature is raised to \(223.0^{\circ} \mathrm{C}\) and the piston moves until it is again in equilibrium?
About how long will it take a perfume molecule to diffuse a distance of $5.00 \mathrm{m}\( in one direction in a room if the diffusion constant is \)1.00 \times 10^{-5} \mathrm{m}^{2} / \mathrm{s} ?$ Assume that the air is perfectly still-there are no air currents.
At \(0.0^{\circ} \mathrm{C}\) and \(1.00 \mathrm{atm}, 1.00 \mathrm{mol}\) of a gas occupies a volume of \(0.0224 \mathrm{m}^{3} .\) (a) What is the number density? (b) Estimate the average distance between the molecules. (c) If the gas is nitrogen \(\left(\mathrm{N}_{2}\right),\) the principal component of air, what is the total mass and mass density?
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