If the density of a gas is 1.2 L at 945 torr and 30. ˚C, what is its molar mass?
P*molar mass = density*RT
Plug in the numbers and solve for molar mass. Remember to use temperature in kelvin. Post your work if you get stuck.
To find the molar mass of a gas, we can use the ideal gas law equation which is given by:
PV = nRT
where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the ideal gas constant
T is the temperature of the gas in Kelvin
In this case, we are given the density of the gas, which is 1.2 L. Density is defined as mass/volume. Since we know the volume, we can calculate the mass.
First, let's convert the temperature from Celsius to Kelvin. The formula to convert Celsius to Kelvin is as follows:
T(K) = T(°C) + 273.15
So, T(K) = 30 °C + 273.15 = 303.15 K
Now, let's calculate the number of moles (n) using the ideal gas law:
PV = nRT
We are given the pressure (945 torr), volume (1.2 L), temperature (303.15 K), and the ideal gas constant (R = 0.0821 L·atm/K·mol). However, we need to convert the pressure from torr to atm since the ideal gas constant is in terms of atm.
1 atm = 760 torr
So, the pressure in atm is calculated as:
P(atm) = 945 torr / 760 torr/atm = 1.24 atm
Now, we can solve for the number of moles:
n = PV / RT
n = (1.24 atm) * (1.2 L) / (0.0821 L·atm/K·mol * 303.15 K)
n ≈ 0.062 moles
Finally, let's calculate the molar mass (M) using the formula:
M = mass / moles
Since we know the density is defined as mass/volume, we can rearrange that formula to solve for mass:
mass = density * volume
mass = 1.2 L * 0.062 moles
mass ≈ 0.0744 grams
Now, we can calculate the molar mass:
M = mass / moles
M = 0.0744 g / 0.062 moles
M ≈ 1.20 g/mol
Therefore, the molar mass of the gas is approximately 1.20 g/mol.