The gaseous product of a reaction is collected in a 30.0 L container at 37 degrees C. The pressure in the container is 2.5 atm and the gas has a mass of 85.0 grams. What is the molar mass of this gas?
I know the correct answer is 28.8 g/mol but I need to know how to get the answer and which gas law you would use?
Use PV = nRT and solve for n = number of mols of gas. Don't forget T must be in kelvin. Then n = grams/molar mass. You know grams and n, solve for molar mass.
To find the molar mass of the gas, we need to use the ideal gas law equation:
PV = nRT
Where:
P = Pressure (in atm)
V = Volume (in liters)
n = number of moles of gas
R = Ideal Gas Constant (0.0821 L.atm/mol.K)
T = temperature in Kelvin
First, we need to convert the given temperature in degrees Celsius to Kelvin:
T (Kelvin) = T (Celsius) + 273.15
T = 37 + 273.15
T = 310.15 K
Now let's rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
Plug in the given values into the equation:
n = (2.5 atm) (30.0 L) / ((0.0821 L.atm/mol.K) * (310.15 K))
n = 2.5 * 30.0 / (0.0821 * 310.15)
n ≈ 0.301 mol
To find the molar mass, we divide the mass of the gas (85.0 grams) by the number of moles:
Molar Mass (g/mol) = Mass (g) / Moles (mol)
Molar Mass ≈ 85.0 g / 0.301 mol ≈ 28.24 g/mol
Therefore, the molar mass of the gas is approximately 28.24 g/mol.
To find the molar mass of the gas, we can use the ideal gas law, which states:
PV = nRT
Where:
P is the pressure of the gas in atmospheres (atm)
V is the volume of the gas in liters (L)
n is the number of moles of the gas
R is the ideal gas constant (0.0821 L·atm/mol·K)
T is the temperature of the gas in Kelvin (K)
In this case, we are given:
P = 2.5 atm
V = 30.0 L
T = 37 degrees Celsius or 310 Kelvin (since Celsius to Kelvin conversion is done by adding 273.15)
First, let's rearrange the equation to solve for n:
n = PV / RT
Now, let's substitute the values:
n = (2.5 atm * 30.0 L) / (0.0821 L·atm/mol·K * 310 K)
n = 2.5 * 30.0 / (0.0821 * 310)
n ≈ 2.92 moles
Next, we'll calculate the molar mass by dividing the mass of the gas by the number of moles:
molar mass = mass of gas / number of moles
Given the mass of the gas is 85.0 grams and the number of moles is 2.92 moles:
molar mass = 85.0 g / 2.92 mol
molar mass ≈ 29.1 g/mol (rounded to one decimal place)
Therefore, the molar mass of this gas is approximately 29.1 g/mol, which is slightly different from the given answer of 28.8 g/mol. It's possible that there was a slight rounding error, or there might be additional significant figures in the given answer.