Question

What is the volume of 15 moles of CO₂ at 50∘C and 800 torr?

Answer 1

The volume of 15 moles of CO₂ at 50°C and 800 torr is approximately
`\(380.16 \text{ liters}\).`

To find the volume of a gas, use the ideal gas law formula: 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

Given:

n = 15 moles

T =
`\(50^\circ C = 50 + 273.15 = 323.15\)` K (temperature in Kelvin)

P = 800 torr (pressure)

Convert pressure to atm:
`\(1 \text{ atm} = 760 \text{ torr}\)`

`\(800 \text{ torr} = (800)/(760) \text{ atm} \approx 1.05 \text{ atm}\)`

Now, rearrange the ideal gas law to solve for volume (V):

`\[PV = nRT\]`

`\[V = (nRT)/(P)\]`

Substitute the given values:

`\[V = \frac{15 \text{ mol} * 0.0821 \text{ L atm/mol K} * 323.15 \text{ K}}{1.05 \text{ atm}}\]`

Calculate the volume:

`\[V \approx (399.17225)/(1.05) \approx 380.16 \text{ L}\]`