A piece of dry ice (solid carbon dioxide) with a mass of \(20.0 \mathrm{~g}\) is placed in a 25.0-L vessel that already contains air at \(50.66 \mathrm{kPa}\) and \(25^{\circ} \mathrm{C}\). After the carbon dioxide has totally sublimed, what is the partial pressure of the resultant \(\mathrm{CO}_{2}\) gas, and the total pressure in the container at \(25^{\circ} \mathrm{C} ?\)

\(n_{CO_2} = 0.454 \mathrm{~mol}\) Step 2: Find the partial pressure of carbon dioxide #tag_title#Determine the partial pressure of the carbon dioxide gas #tag_content# Use the Ideal Gas Law equation, \(PV = nRT\), where \(P\) is the pressure, \(V\) is the volume, \(n\) is the number of moles, \(R\) is the Ideal Gas Constant (\(8.314 \mathrm{J/mol\cdot K}\)), and \(T\) is the temperature in Kelvin. First, convert the temperature from Celsius to Kelvin: \(T = 25^{\circ} \mathrm{C} + 273.15 = 298.15 \mathrm{K}\) Now, rearrange the Ideal Gas Law equation to find the pressure: \(P_{CO_2} = \frac{n_{CO_2}RT}{V}\) Calculate the partial pressure of carbon dioxide: \(P_{CO_2} = \frac{(0.454 \mathrm{~mol})(8.314 \mathrm{J/mol\cdot K})(298.15 \mathrm{K})}{25.0 \mathrm{~L}}\) \(P_{CO_2} = 45.75 \mathrm{kPa}\) Step 3: Calculate the total pressure in the container #tag_title#Determine the total pressure in the container #tag_content# Now, simply add the partial pressures of the air and carbon dioxide to find the total pressure. The air pressure is given as \(50.66\ \mathrm{kPa}\): \(P_{total} = P_{air} + P_{CO_2}\) \(P_{total} = 50.66 \mathrm{kPa} + 45.75 \mathrm{kPa}\) \(P_{total} = 96.41 \mathrm{kPa}\) So, the partial pressure of the resultant carbon dioxide gas is \(45.75 \mathrm{kPa}\), and the total pressure in the container at \(25^{\circ} \mathrm{C}\) is \(96.41 \mathrm{kPa}\).