A piece of solid carbon dioxide, with a mass of 7.4 g, is placed in a 4.0-L otherwise empty container at 27°C.
(a) What is the pressure in the container after all the carbon dioxide vaporizes?
1.0atm
(b) If 7.4 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?
.97atm
(c) What would be the total pressure in the container after the carbon dioxide vaporizes?
??? atm
a. My calculator reads 1.035 atm which I would round to 1.0 to two s.f.
b. I thought Dalton's law said that the partial pressure of a gas is the pressure of the gas as if it were the only gas in the container. So why would the answer for b and a not be the same?
c. Total pressure = sum partial pressure of each gas.
To find the total pressure in the container after the carbon dioxide vaporizes, we need to consider the initial pressure from the air and the pressure contributed by the carbon dioxide.
First, let's find the pressure contributed by the carbon dioxide:
1. Convert the mass of carbon dioxide (7.4 g) to moles using the molar mass of carbon dioxide (44.01 g/mol).
moles of CO2 = 7.4 g / 44.01 g/mol = 0.168 mol
2. Use the ideal gas law equation to find the pressure contributed by the carbon dioxide:
PV = nRT
P_CO2 * V = n_CO2 * R * T
where:
P_CO2 - pressure of carbon dioxide
V - volume of the container (4.0 L)
n_CO2 - moles of carbon dioxide (0.168 mol)
R - ideal gas constant (0.0821 L·atm/(mol·K))
T - temperature in Kelvin (27°C = 27 + 273 = 300 K)
P_CO2 = (n_CO2 * R * T) / V
P_CO2 = (0.168 mol * 0.0821 L·atm/(mol·K) * 300 K) / 4.0 L
P_CO2 = 0.315 atm
Next, let's calculate the total pressure in the container:
(a) In the first case where the container was initially empty, the carbon dioxide will exert its pressure alone. So, the total pressure will be equal to the pressure of carbon dioxide.
Answer: The total pressure in the container after the carbon dioxide vaporizes is 0.315 atm.
(b) In the second case where the container already contains air at 740 torr, we need to convert the pressure of air to atm.
1 atm = 760 torr
740 torr / 760 torr/atm = 0.974 atm
The partial pressure of carbon dioxide is the additional pressure exerted by the carbon dioxide on top of the initial air pressure.
Partial pressure of CO2 = Total pressure - Initial air pressure
Partial pressure of CO2 = 0.974 atm - 0.315 atm
Partial pressure of CO2 = 0.659 atm
Answer: The partial pressure of carbon dioxide in the second case is 0.659 atm.
(c) The total pressure in the container after the carbon dioxide vaporizes in the second case can be obtained by adding the partial pressure of carbon dioxide to the initial air pressure.
Total pressure = Initial air pressure + Partial pressure of CO2
Total pressure = 0.974 atm + 0.315 atm
Total pressure = 1.289 atm (rounded to three decimal places)
Answer: The total pressure in the container after the carbon dioxide vaporizes in the second case is 1.289 atm.