To calculate the volume of a gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal gas constant (0.0821 L·atm/(mol·K))
T = Temperature in Kelvin
First, we need to convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 27°C + 273.15
T(K) = 300.15 K
Next, we can substitute the given values into the ideal gas law equation and solve for V:
PV = nRT
V = (nRT) / P
Given:
n = 0.5 mole
R = 0.0821 L·atm/(mol·K)
T = 300.15 K
P = 750 mmHg (which can be converted to atm by dividing by 760 mmHg/atm)
P = 750 mmHg / 760 mmHg/atm
P = 0.9868 atm
Substituting the values into the equation:
V = (0.5 mol * 0.0821 L·atm/(mol·K) * 300.15 K) / 0.9868 atm
V ≈ 12.72 L
Therefore, the volume of 0.5 mole of carbon dioxide gas at 27°C and 750 mmHg is approximately 12.72 liters.