if 48.3 g of an unknown gas occupies 10.0 L at 40 degrees celsius and 3.10 atm, what is the molar mass of the gas?

PV = nRT and solve for n = number of moles. Then n = grams/molar mass. You know n and grams, solve for molar mass. Remember T must be in kelvin.

To find the molar mass of the gas, we can use the ideal gas law equation, which relates the pressure, volume, temperature, and molar mass of a gas. The ideal gas law equation is given by:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

First, we need to convert the temperature from Celsius to Kelvin. The Kelvin temperature is obtained by adding 273.15 to the Celsius temperature. Therefore, in this case, the temperature is:

40 degrees Celsius + 273.15 = 313.15 Kelvin

Now, we need to rearrange the ideal gas law equation to solve for the number of moles (n) of gas:

n = (PV) / (RT)

Substituting the given values:

P = 3.10 atm
V = 10.0 L
R = 0.0821 L·atm/(mol·K) (the ideal gas constant)
T = 313.15 K

n = (3.10 atm * 10.0 L) / (0.0821 L·atm/(mol·K) * 313.15 K)

Simplifying the equation:

n = 1.248 mol

Now, to find the molar mass of the gas, we divide the mass of the gas by the number of moles:

molar mass = mass / moles

Given mass = 48.3 g and moles = 1.248 mol:

molar mass = 48.3 g / 1.248 mol

Calculating the molar mass:

molar mass = 38.74 g/mol

Therefore, the molar mass of the gas is 38.74 g/mol.