A sample of 0.255 mole of gas has a volume of 748 mL at 28C. Calculate the pressure of this gas.
To calculate the pressure of a gas, we can use the Ideal Gas Law equation:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of the gas
R = ideal gas constant (0.0821 L·atm/(K·mol))
T = temperature of the gas in Kelvin
First, let's convert the temperature from Celsius to Kelvin. To do that, we add 273.15 to the Celsius temperature:
T = 28°C + 273.15 = 301.15 K
Next, we plug in the given values into the Ideal Gas Law equation:
PV = nRT
P * 748 mL = 0.255 mol * 0.0821 L·atm/(K·mol) * 301.15 K
Notice that we need to convert the volume from milliliters (mL) to liters (L) because the gas constant is in liters (L). To do that, we divide the volume by 1000:
P * (748 mL / 1000) = 0.255 mol * 0.0821 L·atm/(K·mol) * 301.15 K
P * 0.748 L = 0.255 mol * 0.0821 L·atm/(K·mol) * 301.15 K
Now we can solve for P by dividing both sides of the equation by 0.748 L:
P = (0.255 mol * 0.0821 L·atm/(K·mol) * 301.15 K) / 0.748 L
P ≈ 8.32 atm
Therefore, the pressure of the gas is approximately 8.32 atm.