what is the molar mass of a gas if 26.0L of the gas has a mass of 43.6g at 1.10 atm and 10.0 C?
Use PV = nRT to solve for n, then n = grams/molar mass.
To find the molar mass of a gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant
T = temperature in Kelvin
First, let's convert the given values:
- Pressure (P) = 1.10 atm
- Volume (V) = 26.0 L
- Mass (m) = 43.6 g
- Temperature (T) = 10.0 °C = 10.0 + 273.15 = 283.15 K
Next, we need to find the number of moles (n) using the mass and molar mass of the gas. The equation to calculate the number of moles is:
n = molar mass / molar mass
Rearranging this equation, we have:
molar mass = (mass x R) / (P x V x T)
Substituting the given values into the equation, we get:
molar mass = (43.6 g x 0.0821 L·atm/(mol·K)) / (1.10 atm x 26.0 L x 283.15 K)
Calculating this expression will give us the molar mass of the gas.
To find the molar mass of a gas, we can use the ideal gas law, which relates the pressure, volume, temperature, and number of moles of a gas.
The ideal gas law is given by the equation: PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
In this case, we are given the pressure (1.10 atm), volume (26.0 L), and temperature (10.0°C = 283.15 K).
First, we need to convert temperature from Celsius to Kelvin. This is done by adding 273.15 to the Celsius value.
T = 10.0°C + 273.15 = 283.15 K
Now, let's rearrange the ideal gas law to solve for the number of moles (n):
n = PV / RT
Substituting the values into the equation:
n = (1.10 atm) * (26.0 L) / (0.0821 L·atm/(mol·K) * 283.15 K)
n ≈ 1.10 * 26.0 / (0.0821 * 283.15)
Now, calculate the value of n.
n ≈ 0.1205 mol
Next, we need to find the molar mass of the gas. The molar mass is the mass of one mole of the substance. It is calculated in grams per mole (g/mol).
To find the molar mass, we need to divide the mass of the gas (43.6g) by the number of moles (0.1205 mol).
Molar mass = mass / moles
Molar mass ≈ 43.6 g / 0.1205 mol
Now, calculate the molar mass.
Molar mass ≈ 361.7 g/mol
Therefore, the molar mass of the gas is approximately 361.7 g/mol.