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Chapter 10: Problem 41

A \(50.0 \mathrm{~g}\) sample of solid \(\mathrm{CO}_{2}\) (dry ice) is added at \(-100^{\circ} \mathrm{C}\) to an evacuated (all of the gas removed) container with a volume of \(5.0 \mathrm{~L}\). If the container is sealed and then allowed to warm to room temperature \(\left(25^{\circ} \mathrm{C}\right)\) so that the entire solid \(\mathrm{CO}_{2}\) is converted to a gas, what is the pressure inside the container?

Short Answer

Expert verified
The pressure inside the container after the CO₂ solid has been converted to gas at room temperature (25°C) is approximately \(9.116 atm\).

Step by step solution

01

Convert mass to moles

To begin, calculate the number of moles (n) of CO₂ in the container by dividing the given mass (50.0 grams) by the molar mass of CO₂ (44.01 g/mol). n = mass (m) / molar mass (M) n = (50.0 g) / (44.01 g/mol)
02

Convert temperatures from Celsius to Kelvin

The temperatures given are in degrees Celsius, but we need to use Kelvin when working with the Ideal Gas Law equation. Convert both starting and final temperatures to Kelvin: T1 = -100°C + 273.15 = 173.15 K T2 = 25°C + 273.15 = 298.15 K
03

Apply Ideal Gas Law equation

Now, we can use the Ideal Gas Law equation, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature in Kelvin. Given: V = 5.0 L, R = 0.0821 L atm/mol K, and T = 298.15 K We are asked to find the pressure (P) inside the container after all CO₂ is converted to gas at 25°C (298.15 K). Plug in the known values and solve for P: P = (nR * T) / V
04

Calculate Pressure

Using information from Steps 1-3, calculate the pressure in the container: P = ((50.0 g / 44.01 g/mol) * (0.0821 L atm/mol K) * (298.15 K)) / (5.0 L) P = 9.116 atm The pressure inside the container after the CO₂ solid has been converted to gas will be approximately 9.116 atm.

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Most popular questions from this chapter

(a) Calculate the density of sulfur hexafluoride gas at 94.26 \(\mathrm{kPa}\) and \(21{ }^{\circ} \mathrm{C}\). (b) Calculate the molar mass of a vapor that has a density of \(7.135 \mathrm{~g} / \mathrm{L}\) at $12{ }^{\circ} \mathrm{C}\( and \)99.06 \mathrm{kPa}$..

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