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Chapter 6: Problem 32

What is the pressure, in pascals, exerted by \(1242 \mathrm{g}\) CO(g) when confined at \(-25^{\circ} \mathrm{C}\) to a cylindrical tank \(25.0 \mathrm{cm}\) in diameter and \(1.75 \mathrm{m}\) high?

Short Answer

Expert verified
The pressure exerted by the CO(g) in the tank is 115065 Pa or 115 kPa.

Step by step solution

01

Calculate the number of moles

The molar mass of CO(g) is \(28.01 g/mol\). Using this, the number of moles (\(n\)) can be calculated using the formula \(n = \frac{mass}{molar \, mass}\), so \(n = \frac{1242g}{28.01 g/mol} = 44.34 mol\).
02

Calculate the volume of the tank

The volume of a cylinder is given by \(V= \pi r^2h\), where \(r\) is the radius, and \(h\) is the height. As the diameter is given, the radius \(r = \frac{d}{2} = \frac{25 cm}{2}\). Convert the radius from cm to m as \(r = 0.125 m\) because the volume must be in cubic meters to match the units of the gas constant R. The volume becomes \(V= \pi (0.125 m)^2 \times 1.75 m = 0.086 m^3\).
03

Convert temperature to Kelvin

The temperature is given in Celsius but must be in Kelvin for the Ideal Gas Law, which can be done using the formula \(T(K) = T(°C) + 273.15\). So the temperature is \(-25 °C + 273.15 = 248.15 K\).
04

Use the Ideal Gas Law

The Ideal Gas Law is \(P = \frac{nRT}{V}\), where P is pressure, R is the Ideal gas constant (R = \(8.314 \, J/(mol \cdot K)\)), n is the number of moles, T is the temperature in Kelvin, and V is the volume in cubic meters. Substituting the calculated values in gives \(P = \frac{44.34 mol \times 8.314 J/(mol \cdot K) \times 248.15 K}{0.086 m^3}\)
05

Calculate the pressure

Calculate the pressure by performing the arithmetic to find \(P = 115065 Pa\) or \(115 kPa\). Therefore, the pressure exerted by the CO(g) in the tank is \(115 kPa\) or \(115065 Pa\).

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Most popular questions from this chapter

Aluminum (Al) and iron (Fe) each react with hydrochloric acid solution (HCl) to produce a chloride salt and hydrogen gas, \(\mathrm{H}_{2}(\mathrm{g}) .\) A \(0.1924 \mathrm{g}\) sample of a mixture of \(\mathrm{Al}\) and \(\mathrm{Fe}\) is treated with excess \(\mathrm{HCl}\) solution. A volume of \(159 \mathrm{mL}\) of \(\mathrm{H}_{2}\) gas is collected over water at \(19.0^{\circ} \mathrm{C}\) and 841 Torr. What is the percent (by mass) of Fe in the mixture? The vapor pressure of water at \(19.0^{\circ} \mathrm{C}\) is 16.5 Torr.

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?

If 3.0 L of oxygen gas at \(177^{\circ} \mathrm{C}\) is cooled at constant pressure until the volume becomes \(1.50 \mathrm{L}\), then what is the final temperature?

According to the CRC Handbook of Chemistry and Physics (83rd ed.), the molar volume of \(\mathrm{O}_{2}(\mathrm{g})\) is \(0.2168 \mathrm{Lmol}^{-1}\) at \(280 \mathrm{K}\) and \(10 \mathrm{MPa}\). (Note: \(1 \mathrm{MPa}=\) \(\left.1 \times 10^{6} \mathrm{Pa} .\right)\)(a) Use the van der Waals equation to calculate the pressure of one mole of \(\mathrm{O}_{2}(\mathrm{g})\) at \(280 \mathrm{K}\) if the volume is 0.2168 L. What is the \% error in the calculated pressure? The van der Waals constants are \(a=1.382 \mathrm{L}^{2}\) bar \(\mathrm{mol}^{-2}\) and \(b=0.0319 \mathrm{L} \mathrm{mol}^{-1}\) (b) Use the ideal gas equation to calculate the volume of one mole of \(\mathrm{O}_{2}(\mathrm{g})\) at \(280 \mathrm{K}\) and \(10 \mathrm{MPa}\). What is the \% error in the calculated volume?

A 0.7178 g sample of a hydrocarbon occupies a volume of \(390.7 \mathrm{mL}\) at \(65.0^{\circ} \mathrm{C}\) and \(99.2 \mathrm{kPa}\). When the sample is burned in excess oxygen, \(2.4267 \mathrm{g} \mathrm{CO}_{2}\) and \(0.4967 \mathrm{g} \mathrm{H}_{2} \mathrm{O}\) are obtained. What is the molecular formula of the hydrocarbon? Write a plausible structural formula for the molecule.
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