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Chapter 8: Problem 83

A piece of solid carbon dioxide, with a mass of \(7.8 \mathrm{g},\) is placed in a \(4.0\)-\(\mathrm{L}\) otherwise empty container at \(27^{\circ} \mathrm{C}\). What is the pressure in the container after all the carbon dioxide vaporizes? If \(7.8 \mathrm{g},\) solid carbon dioxide were placed in the same container but it already contained air at \(740\) torr, what would be the partial pressure of carbon dioxide and the total pressure in the container after the carbon dioxide vaporizes?

Short Answer

Expert verified
The pressure in the container after all the carbon dioxide vaporizes is 3.44 atm (or 2614.4 torr), the partial pressure of carbon dioxide is 1874.4 torr, and the total pressure in the container when it already contained air at 740 torr is 2614.4 torr.

Step by step solution

01

1. Convert temperature to Kelvin

To work with the Ideal Gas Law, we need to convert the given temperature from Celsius to Kelvin. We can do this using the formula: \(T(K)= T(°C) + 273.15\). \(T(K) = 27°C + 273.15 = 300.15 K\)
02

2. Convert mass of carbon dioxide to moles

We need to convert the mass of carbon dioxide (7.8 g) to moles using the molar mass of CO₂. The molar mass of CO₂ is approximately 44.01 g/mol. \(n = \frac{m}{M} = \frac{7.8 \, \text{g}}{44.01\, \text{g/mol}} = 0.177 \, \text{moles}\)
03

3. Calculate pressure before adding air

Now that we have all the necessary information, we can apply the Ideal Gas Law to find the pressure in the container after the carbon dioxide vaporizes before adding any air: \(P = \frac{nRT}{V} = \frac{0.177 \, \text{moles} \times 0.0821\, \frac{\text{L} \cdot \text{atm}}{\text{mol} \cdot \text{K}} \times 300.15\, \text{K}}{4.0\, \text{L}} = 3.44 \, \mathrm{atm}\)
04

4. Convert pressure to torr

The asked pressure in the next step is given in torr, so we need to convert our pressure in atm to torr using the conversion factor: 1 atm = 760 torr. \(P_\text{before} = 3.44\, \text{atm} \times \frac{760 \, \text{torr}}{1 \, \text{atm}} = 2614.4 \, \text{torr}\)
05

5. Calculate partial pressure of carbon dioxide

The container already has a pressure due to air (740 torr). We can now find the partial pressure of carbon dioxide by subtracting this pressure from the total pressure calculated before. \(P_\text{CO₂} = P_\text{before} - P_\text{air} = 2614.4\, \text{torr} - 740\, \text{torr} = 1874.4\, \text{torr}\)
06

6. Calculate the total pressure

Finally, we will calculate the total pressure of the container after adding the initial air pressure (740 torr) to the partial pressure of carbon dioxide. \(P_\text{total} = P_\text{CO₂} + P_\text{air} = 1874.4\, \text{torr} + 740\, \text{torr} = 2614.4\, \text{torr}\) So, the pressure in the container after all the carbon dioxide vaporizes is 3.44 atm (or 2614.4 torr), the partial pressure of carbon dioxide is 1874.4 torr, and the total pressure in the container when it already contained air at 740 torr is 2614.4 torr.

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Most popular questions from this chapter

At \(0^{\circ} \mathrm{C}\) a \(1.0\)-\(\mathrm{L}\) flask contains \(5.0 \times 10^{-2}\) mole of \(\mathrm{N}_{2}, 1.5 \times\) \(10^{2} \mathrm{mg} \mathrm{O}_{2},\) and \(5.0 \times 10^{21}\) molecules of \(\mathrm{NH}_{3} .\) What is the partial pressure of each gas, and what is the total pressurelin the flask?

The nitrogen content of organic compounds can be determined by the Dumas method. The compound in question is first reacted by passage over hot \(\mathrm{CuO}(s)\) : $$\text { Compound } \longrightarrow\mathrm{N}_{2}(g)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$$ The product gas is then passed through a concentrated solution of KOH to remove the \(\mathrm{CO}_{2}\). After passage through the KOH solution, the gas contains \(\mathrm{N}_{2}\) and is saturated with water vapor. In a given experiment a \(0.253-g\) sample of a compound produced \(31.8 \mathrm{mL} \mathrm{N}_{2}\) saturated with water vapor at \(25^{\circ} \mathrm{C}\) and \(726\) torr. What is the mass percent of nitrogen in the compound? (The vapor pressure of water at \(25^{\circ} \mathrm{C}\) is 23.8 torr.)

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