Gas Laws and Molar Volume Calculation

What is the molar volume of CO2 at 39 C and 652 torr?

How can we calculate the molar volume of CO2 using the ideal gas law?

Answer:

The molar volume of CO2 at 39°C and 652 torr is 24.45 L/mol.

The molar volume of a gas can be calculated using the ideal gas law:

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 gas, R is the ideal gas constant (0.08206 L·atm/mol·K), and T is the temperature of the gas in Kelvin (K).

To solve for the molar volume of CO2 at 39°C (312 K) and 652 torr (0.859 atm), we can rearrange the ideal gas law as follows:

V = (nRT) / P

First, we need to calculate the number of moles of CO2. We can use the following equation, which relates the pressure, volume, number of moles, and temperature of a gas:

PV = nRT

Solving for n, we get:

n = (PV) / (RT)

Substituting the given values, we get:

n = (0.859 atm * V) / (0.08206 L·atm/mol·K * 312 K)

Now we can substitute this expression for n into the equation for the molar volume:

V = (nRT) / P

V = [(0.859 atm * V) / (0.08206 L·atm/mol·K * 312 K)] * (0.08206 L·atm/mol·K * 312 K) / (0.859 atm)

Simplifying, we get:

V = 24.45 L/mol

Therefore, the molar volume of CO2 at 39°C and 652 torr is 24.45 L/mol.