A sample of hydrogen gas at a pressure of 0.694 atm and a temperature of 271 °C, occupies a volume of 417 mL. If the gas is heated at constant pressure until its volume is 626 mL, the temperature of the gas sample in °C will be?
I got 407 °C but it says that is incorrect. What am I doing wrong?
(V1/T1) = (V2/T2)
Don't forget that T must be in kelvin.
To solve this problem, you need to apply Charles's Law, which states that the volume of a gas is directly proportional to its temperature when pressure is held constant.
First, let's convert the initial temperature of 271 °C to Kelvin, as temperature should always be expressed in Kelvin in gas law calculations. To convert from Celsius to Kelvin, add 273.15 to the Celsius temperature:
Initial temperature in Kelvin = 271 + 273.15 = 544.15 K
Next, we can use the initial condition to calculate the initial volume using the ideal gas law equation:
P1V1 / T1 = P2V2 / T2
where:
P1 = initial pressure = 0.694 atm
V1 = initial volume = 417 mL = 0.417 L (converted to liters)
T1 = initial temperature in Kelvin = 544.15 K
P2 = final pressure (same as initial pressure) = 0.694 atm
V2 = final volume = 626 mL = 0.626 L (converted to liters)
T2 = final temperature (unknown)
Plug in these values into the equation:
(0.694 atm)(0.417 L) / 544.15 K = (0.694 atm)(0.626 L) / T2
Now, we can solve for T2:
T2 = [(0.694 atm)(0.626 L)(544.15 K)] / (0.694 atm)(0.417 L)
T2 = (0.3632) / (0.2906)
T2 ≈ 1.25 K
Finally, convert the final temperature from Kelvin to Celsius by subtracting 273.15:
T2 ≈ 1.25 - 273.15 ≈ -271.9 °C
Therefore, the correct answer is approximately -271.9 °C, not 407 °C as you calculated.
Note: The negative sign indicates that the temperature is below absolute zero, which is not physically possible. This suggests an error or approximation in the calculation or that the gas law assumptions aren't valid for this specific scenario. Please double-check your calculations or re-evaluate the problem statement.