Question

2.00 moles of a gas occupies 62.2 L at a particular temperature and pressure. It's density 0.900 g/L. The standard molar volume is 22.4 L. What is the molar mass?

Answer 1

27.99 g/mol.

Step-by-step explanation:

First, let's calculate the mass of 2.00 moles of the gas using the density:

Mass = Volume x Density

Mass = 62.2 L x 0.900 g/L

Mass = 55.98 g

Next, let's calculate the volume of 2.00 moles of the gas at STP (standard temperature and pressure):

2.00 moles x (22.4 L/1 mole) = 44.8 L

Now we can use the ideal gas law to find the molar mass:

PV = nRT

where:

P = pressure = ? (not given)

V = volume = 44.8 L

n = moles = 2.00 mol

R = gas constant = 0.0821 L·atm/(mol·K)

T = temperature

Let's assume the pressure is also at STP (1 atm), so we can use that value for P:

(1 atm)(44.8 L) = (2.00 mol)(0.0821 L·atm/(mol·K))(273 K)

Solving for T:

T = (1 atm)(44.8 L) / (2.00 mol)(0.0821 L·atm/(mol·K))

T = 544 K

Now we can use the ideal gas law again to solve for the molar mass:

PV = nRT

where:

P = pressure = 1 atm

V = volume = 62.2 L

n = moles = 2.00 mol

R = gas constant = 0.0821 L·atm/(mol·K)

T = temperature = 544 K

Solving for the pressure:

P = (nRT) / V

P = (2.00 mol)(0.0821 L·atm/(mol·K))(544 K) / 62.2 L

P = 8.87 atm

Now we can use the density to find the molar mass:

density = mass / volume

0.900 g/L = 55.98 g / 62.2 L

Solving for the volume of 1 mole of the gas:

0.900 g/L = 55.98 g / V

V = 62.2 L / 0.900 mol/L

V = 69.1 L/mol

Finally, we can calculate the molar mass:

molar mass = mass / moles

molar mass = 55.98 g / 2.00 mol

molar mass = 27.99 g/mol

Therefore, the molar mass of the gas is 27.99 g/mol.