A piece of solid carbon dioxide, with a mass of 6.2 g, is placed in a 4.0 L otherwise empty container at 21°C.
(
a) What is the pressure in the container after all the carbon dioxide vaporizes?
atm (.86 atm)
(b) If 6.2 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?
in atm
(c) What would be the total pressure in the container after the carbon dioxide vaporizes?
in atm
yugioh!!!!!
To solve these problems, we can 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, and T is the temperature in Kelvin.
To start, we need to calculate the number of moles of carbon dioxide present in the given mass.
(a) To find the pressure after all the carbon dioxide vaporizes, we need to know the number of moles. We can use the molar mass of carbon dioxide to convert the given mass to moles.
The molar mass of carbon dioxide (CO2) is 44.01 g/mol.
Number of moles = mass / molar mass
= 6.2 g / 44.01 g/mol
≈ 0.1406 mol
Since the carbon dioxide vaporizes completely, the number of moles of carbon dioxide gas equals the number of moles provided above.
Now, let's calculate the pressure.
P = nRT / V
Given:
n = 0.1406 mol
R = 0.0821 L·atm/(mol·K)
V = 4.0 L
T = 21°C = 294 K (convert Celsius to Kelvin)
P = (0.1406 mol)(0.0821 L·atm/(mol·K))(294 K) / 4.0 L
P ≈ 0.86 atm
Therefore, the pressure in the container after all the carbon dioxide vaporizes is approximately 0.86 atm.
(b) To find the partial pressure of carbon dioxide, we'll add the pressure of the air (given in torr) to the pressure calculated in part (a).
Given:
P_air = 740 torr = 740/760 atm (converting torr to atm)
Partial pressure of carbon dioxide = Pressure (from part (a)) + P_air
Partial pressure of carbon dioxide ≈ 0.86 atm + (740/760) atm
(c) To find the total pressure in the container after the carbon dioxide vaporizes, we need to add the partial pressure of carbon dioxide to the pressure of the air.
Total pressure = partial pressure of carbon dioxide + P_air
Total pressure ≈ (0.86 atm + (740/760) atm) + (740/760) atm
To answer these questions, we can use the ideal gas law, which states that the pressure of a gas is directly proportional to its temperature, volume, and the number of moles of the gas. The formula for the ideal gas law is:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
Before we start, we need to convert the given values to appropriate units. The ideal gas constant, R, is 0.0821 L·atm/(mol·K). The temperature, T, needs to be converted to Kelvin by adding 273.15 to the Celsius value.
(a) To find the pressure in the container after all the carbon dioxide vaporizes:
First, we need to calculate the number of moles of carbon dioxide. The molar mass of carbon dioxide (CO2) is 44.01 g/mol.
n = mass / molar mass
n = 6.2 g / 44.01 g/mol
Next, we can substitute the values into the ideal gas law equation:
PV = nRT
P * 4.0 L = (6.2 g / 44.01 g/mol) * (0.0821 L·atm/(mol·K)) * (21°C + 273.15 K)
Solving for P:
P = [(6.2 g / 44.01 g/mol) * (0.0821 L·atm/(mol·K)) * (21°C + 273.15 K)] / 4.0 L
After evaluating the equation, we find that P is approximately 0.86 atm.
(b) To find the partial pressure of carbon dioxide when 6.2 g of solid carbon dioxide is placed in the container already containing air at 740 torr:
First, we need to convert the given pressure to atm. There are 760 torr in 1 atm, so 740 torr is equal to 740/760 atm.
Now, we can substitute the values into the ideal gas law equation:
P * 4.0 L = (6.2 g / 44.01 g/mol) * (0.0821 L·atm/(mol·K)) * (21°C + 273.15 K)
Since we want to find the partial pressure of carbon dioxide, we can rearrange the equation:
P = [(6.2 g / 44.01 g/mol) * (0.0821 L·atm/(mol·K)) * (21°C + 273.15 K)] / 4.0 L
After evaluating the equation, we have P as the partial pressure of carbon dioxide in atm.
(c) To find the total pressure in the container after the carbon dioxide vaporizes:
We can simply sum up the partial pressure of carbon dioxide and the pressure of the existing air.
Total Pressure = Partial Pressure of CO2 + Pressure of Air
Substituting the values:
Total Pressure = P + (740 torr / 760 torr)
We convert the pressure of air from torr to atm by dividing by 760.
After evaluating the equation, we have the total pressure in atm.
a) I found 0.86 atm
b)I'm assuming the CO2 vaporizes completely. Won't the partial pressure of the CO2 be the same as in (a)? Dalton's Law tells us that the total pressure is the sum of the partial pressures of each gas and each gas will exert a pressure as if the other gas were not present. Check my thinking. OR, try PV = nRT to calculate pCO2 (done in part a), then calcualte pressure of air (740/760) and add them together. Then determine mols CO2 and mols air, add them together and use PV = nRT to calculate total pressure. That should be the same total as you obtained when you added the partial pressure of each.
c)explained in (b)