A piece of solid carbon dioxide, with a mass of 6.8 g, is placed in a 4.0 L otherwise empty container at 23°C.
a) What is the pressure in the container after all the carbon dioxide vaporizes?
b)If 6.8 g solid carbon dioxide were placed in the same container but it already contained air at 740 torr, what would be the partial pressure PCO2 of carbon dioxide?
c)What would be the total pressure Ptotal in the container after the carbon dioxide vaporized?
To answer these questions, we need to understand the ideal gas law equation, which relates the pressure, volume, temperature, and number of moles of a gas. The ideal gas law equation is written as:
PV = nRT
where:
P is the pressure
V is the volume
n is the number of moles
R is the ideal gas constant (0.0821 L·atm/mol·K)
T is the temperature in Kelvin
First, let's convert the temperature from Celsius to Kelvin by adding 273 to the given temperature of 23°C:
T = 23°C + 273 = 296 K
a) What is the pressure in the container after all the carbon dioxide vaporizes?
To find the pressure after the carbon dioxide vaporizes, we need to calculate the number of moles of carbon dioxide.
1. Calculate the number of moles (n) using the formula:
n = mass / molar mass
The molar mass of carbon dioxide (CO2) is 44.01 g/mol.
n = 6.8 g / 44.01 g/mol
n = 0.1547 mol
2. Now, substitute the values into the ideal gas law equation:
PV = nRT
P * 4.0 L = (0.1547 mol) * (0.0821 L·atm/mol·K) * (296 K)
P = (0.1547 mol * 0.0821 L·atm/mol·K * 296 K) / 4.0 L
P ≈ 2.81 atm
Therefore, the pressure in the container after all the carbon dioxide vaporizes is approximately 2.81 atm.
b) If 6.8 g solid carbon dioxide were placed in the same container but it already contained air at 740 torr, what would be the partial pressure PCO2 of carbon dioxide?
Since we are adding the solid carbon dioxide to a container with air, the total pressure will be the sum of the partial pressures of carbon dioxide and air.
1 atm = 760 torr (to convert between torr and atm)
Partial pressure of carbon dioxide (PCO2) = total pressure - partial pressure of air
Partial pressure of air = 740 torr / 760 torr/atm = 0.974 atm
Partial pressure of carbon dioxide = 2.81 atm - 0.974 atm
PCO2 ≈ 1.84 atm
Therefore, the partial pressure of carbon dioxide (PCO2) would be approximately 1.84 atm.
c) What would be the total pressure (Ptotal) in the container after the carbon dioxide vaporized?
Since the carbon dioxide completely vaporizes, it will occupy the entire volume of the container. Therefore, the total pressure will only be determined by the partial pressure of carbon dioxide.
Thus, the total pressure (Ptotal) in the container after the carbon dioxide vaporizes would be approximately 2.81 atm.