To determine the volume of a gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = Pressure (in atmospheres)
V = Volume (in liters)
n = Number of moles
R = Ideal gas constant (0.0821 L·atm/(mol·K))
T = Temperature (in Kelvin)
First, let's convert the given pressure from mmHg to atm:
1 atm = 760 mmHg
So, the pressure is 828 mmHg * (1 atm / 760 mmHg) = 1.0895 atm.
Now, we need to convert the given temperature from degrees Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 26.8 °C + 273.15 = 299.95 K.
Next, let's substitute the known values into the ideal gas law equation:
V = (nRT) / P
V = (0.0315 mol * 0.0821 L·atm/(mol·K) * 299.95 K) / 1.0895 atm
V = 0.7509 L
Finally, let's convert the volume from liters to milliliters:
V(mL) = V(L) * 1000
V(mL) = 0.7509 L * 1000 = 750.9 mL
Therefore, the volume of 0.0315 mol of the gas at 828 mmHg and 26.8 °C is approximately 750.9 mL