A gas occupies a volume of exactly 500 mL at STP. What volume would it occupy at exactly 70°C and 400 mm of pressure?
To find the new volume of the gas at 70°C and 400 mm of pressure, we can use the combined gas law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure of the gas = 760 mm (STP pressure)
V1 = initial volume of the gas = 500 mL
T1 = initial temperature of the gas in Kelvin (STP temperature)
P2 = final pressure = 400 mm
T2 = final temperature in Kelvin = 70°C + 273.15 (converting Celsius to Kelvin)
Now we rearrange the equation to solve for V2 (the final volume):
V2 = (P1 * V1 * T2) / (P2 * T1)
Substituting the given values into the equation:
V2 = (760 mm * 500 mL * (70 + 273.15) K) / (400 mm * 273.15 K)
Now let's calculate the final volume of the gas:
V2 = (760 * 500 * (70 + 273.15)) / (400 * 273.15)
V2 ≈ 556.76 mL
Therefore, the gas would occupy approximately 556.76 mL at 70°C and 400 mm of pressure.