A sample of gas with a mass of 1.62 g occupies a volume of 941 mL at a pressure of 748 torr and a temperature of 20.0 C. What is the molar mass of the gas?
42.1
To find the molar mass (M) of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
- P represents the pressure of the gas in atm (convert torr to atm by dividing by 760)
- V represents the volume of the gas in liters (convert mL to liters by dividing by 1000)
- n represents the number of moles of gas
- R represents the ideal gas constant (0.0821 L·atm/mol·K)
- T represents the temperature of the gas in Kelvin (convert °C to K by adding 273.15)
Let's calculate the number of moles of gas (n):
P = 748 torr / 760 torr/atm = 0.983 atm
V = 941 mL / 1000 mL/L = 0.941 L
T = 20.0°C + 273.15 = 293.15 K
Now we can rearrange the ideal gas law equation to solve for n:
n = (PV) / (RT)
n = (0.983 atm * 0.941 L) / (0.0821 L·atm/mol·K * 293.15 K)
n ≈ 0.0372 mol
The molar mass (M) of the gas can be calculated by dividing the mass of the gas by the number of moles:
M = (mass of gas) / (number of moles)
M = 1.62 g / 0.0372 mol
M ≈ 43.55 g/mol
Therefore, the molar mass of the gas is approximately 43.55 g/mol.
To find the molar mass of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atmospheres)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, we need to convert the given values to the appropriate units. The pressure is given in torr, so it needs to be converted to atmospheres. 1 torr is equivalent to 1/760 atm.
P = 748 torr × (1 atm / 760 torr) = 0.983 atm
The volume is given in milliliters, so it needs to be converted to liters. There are 1000 mL in 1 liter.
V = 941 mL × (1 L / 1000 mL) = 0.941 L
The temperature is given in degrees Celsius, so it needs to be converted to Kelvin. The Kelvin scale is 273.15 degrees Celsius higher than the Celsius scale.
T = 20.0°C + 273.15 = 293.15 K
Now, we can substitute the values into the ideal gas law equation:
(0.983 atm)(0.941 L) = n(0.0821 L·atm/(mol·K))(293.15 K)
Solving for n, the number of moles:
0.9193 = n(24.0456)
n = 0.9193 / 24.0456 = 0.0382 moles
Next, we can calculate the molar mass using the equation:
molar mass = mass / number of moles
The mass of the gas is given as 1.62 grams.
molar mass = 1.62 g / 0.0382 mol ≈ 42.36 g/mol
Therefore, the molar mass of the gas is approximately 42.36 g/mol.
Use PV = nRT and solve for n = number of mols. Then n = grams/molar mass and solve for molar mass.
Remember T must be in kelvin, volume in L, and P in atmospheres.