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Chapter 6: Problem 34

At what temperature is the molar volume of an ideal gas equal to \(22.4 \mathrm{L},\) if the pressure of the gas is \(2.5 \mathrm{atm} ?\)

Short Answer

Expert verified
The temperature at which the molar volume of an ideal gas is equal to \(22.4 L\) and the pressure is \(2.5 atm\) is approximately \(684.16 K\).

Step by step solution

01

Understand the data given in the problem

Firstly, understand what is given in the problem. The molar volume, which is the volume per mole, is given as \(22.4 L\). We also know the pressure of the gas is \(2.5 atm\). Given this is a molar volume, we know that n = 1 mole. We're asked to find the temperature at which these conditions are met.
02

Substitution into the Ideal Gas Law formula

Next, substitute these values into the Ideal Gas Law formula, \(PV = nRT\). This means that \(2.5 atm * 22.4L = 1 mole * R * T\). We need to find the temperature T. The value of the ideal gas constant R depends on the units used; in this case, \(0.0821 L.atm/(mol.K)\) should be used.
03

Calculate the temperature

For the final step, rearrange the equation to solve for T: \(T = PV/(nR) = (2.5 atm * 22.4L) / (1 mol * 0.0821 L.atm/(mol.K))\). After performing the calculation, the result is approximately \(684.16 K\).

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Most popular questions from this chapter

Monochloroethylene is used to make polyvinylchloride (PVC). It has a density of \(2.56 \mathrm{g} / \mathrm{L}\) at \(22.8^{\circ} \mathrm{C}\) and 756 mmHg. What is the molar mass of monochloroethylene? What is the molar volume under these conditions?

Which of the following choices represents the molar volume of an ideal gas at \(25^{\circ} \mathrm{C}\) and 1.5 atm? (a) \((298 \times 1.5 / 273) \times 22.4 \mathrm{L} ;\) (b) \(22.4 \mathrm{L}\) (c) \((273 \times 1.5 / 298) \times 22.4 \mathrm{L}\) (d) \([298 /(273 \times 1.5)] \times 22.4 \mathrm{L}\) (e) \([273 /(298 \times 1.5)] \times 22.4 \mathrm{L}\)

A 4.0 L sample of \(\mathrm{O}_{2}\) gas has a pressure of 1.0 atm. A 2.0 L sample of \(\mathrm{N}_{2}\) gas has a pressure of 2.0 atm. If these two samples are mixed and then compressed in a 2.0 L vessel, what is the final pressure of the mixture? Assume that the temperature remains unchanged.

What are the ratios of the diffusion rates for the pairs of gases (a) \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2} ;\) (b) \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{D}_{2} \mathrm{O}\) \(\left(\mathrm{D}=\text { deuterium, i.e., }_{1}^{2} \mathrm{H}\right) ;\) (c) \(^{14} \mathrm{CO}_{2}\) and \(^{12} \mathrm{CO}_{2}\) (d) \(^{235} \mathrm{UF}_{6}\) and \(^{238} \mathrm{UF}_{6} ?\)

A mixture of \(1.00 \mathrm{g} \mathrm{H}_{2}\) and \(8.60 \mathrm{g} \mathrm{O}_{2}\) is introduced into a 1.500 L flask at \(25^{\circ} \mathrm{C}\). When the mixture is ignited, an explosive reaction occurs in which water is the only product. What is the total gas pressure when the flask is returned to \(25^{\circ} \mathrm{C} ?\) (The vapor pressure of water at \(25^{\circ} \mathrm{C}\) is \(23.8 \mathrm{mmHg}\).)
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