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?
a. Use PV = nRT and solve for P.
b. pCO2 will be the same as in a assuming all of it sublimes.
c. pCO2 + 740 mm(keep the units the same) = Ptotal.
To solve these questions, we can use the ideal gas law: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, let's convert the temperature from Celsius to Kelvin. We add 273 to the Celsius temperature.
a) To find the pressure in the container after all the carbon dioxide vaporizes, we need to know the number of moles of carbon dioxide. The molar mass of carbon dioxide (CO2) is 44.01 g/mol.
Step 1: Calculate the number of moles (n) of carbon dioxide.
n = mass / molar mass
n = 6.8g / 44.01g/mol
n ≈ 0.15465 mol (rounded to 5 decimal places)
Step 2: Convert the temperature to Kelvin.
T = 23°C + 273 = 296 K
Step 3: Substitute the values into the ideal gas law and solve for P.
PV = nRT
P = (nRT) / V
P = (0.15465mol * 0.0821 atm·L/mol·K * 296 K) / 4.0 L
P ≈ 3.669 atm (rounded to 3 decimal places)
b) If the container already contains air at a pressure of 740 torr, we need to find the partial pressure of carbon dioxide (PCO2).
Step 1: Convert the pressure of the air from torr to atm.
1 atm = 760 torr
740 torr / 760 torr/atm = 0.974 atm
Step 2: Substitute the values into the ideal gas law and solve for PCO2.
Ptotal = PCO2 + Pair
PCO2 = Ptotal - Pair
PCO2 = 3.669 atm - 0.974 atm
PCO2 ≈ 2.695 atm (rounded to 3 decimal places)
c) To find the total pressure (Ptotal) in the container after the carbon dioxide vaporized, we need to add the partial pressure of carbon dioxide to the pressure of the air.
Ptotal = PCO2 + Pair
Ptotal = 2.695 atm + 0.974 atm
Ptotal ≈ 3.669 atm (rounded to 3 decimal places)
In summary:
a) The pressure in the container after all the carbon dioxide vaporizes is approximately 3.669 atm.
b) The partial pressure of carbon dioxide (PCO2) when 6.8 g of solid carbon dioxide is placed in the container with air at 740 torr is approximately 2.695 atm.
c) The total pressure in the container after the carbon dioxide vaporizes is approximately 3.669 atm.
To solve these questions, we need to apply the Ideal Gas Law, which relates the pressure, volume, temperature, and number of moles of a gas. The equation is given as:
PV = nRT
Where:
- P is the pressure of the gas in atmospheres (atm) or torr (mmHg),
- V is the volume of the container in liters (L),
- n is the number of moles of gas,
- R is the ideal gas constant, which is 0.0821 L∙atm/mol∙K,
- T is the temperature of the gas in Kelvin (K).
Now let's solve each question step by step:
a) What is the pressure in the container after all the carbon dioxide vaporizes?
First, we need to calculate the number of moles of carbon dioxide. To do that, we divide the mass of the solid CO2 by its molar mass. The molar mass of CO2 is approximately 44 g/mol.
Mass of CO2 = 6.8 g
Number of moles of CO2 = (6.8 g) / (44 g/mol)
Next, we need to convert the temperature from Celsius to Kelvin. Remember that Kelvin = Celsius + 273.
Temperature (T) = 23°C + 273 = 296 K
Now, we can substitute the values into the Ideal Gas Law equation:
PV = nRT
P * 4.0 L = [(6.8 g) / (44 g/mol)] * (0.0821 L∙atm/mol∙K) * 296 K
Solving for P, we find:
P = [(6.8 g) / (44 g/mol)] * (0.0821 L∙atm/mol∙K) * 296 K / 4.0 L
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?
In this case, we already have the pressure of the pre-existing air in the container, which is 740 torr. To find the partial pressure of CO2, we need to add it to the existing pressure.
Partial pressure of CO2 = Existing pressure + Pressure due to CO2
Partial pressure of CO2 = 740 torr + Pressure due to CO2
We can use the same approach as in part a to find the pressure due to CO2. So, we calculate the number of moles of CO2 and use the Ideal Gas Law equation.
c) What would be the total pressure (Ptotal) in the container after the carbon dioxide vaporized?
After the CO2 vaporizes, its pressure will be added to the existing pressure in the container. Therefore, the total pressure will be the sum of the existing pressure and the pressure due to the CO2 vaporization.