a gas occupies a volume of 5.00L at 27 degreesC and 742 mmHg. if the volume is held constant and the temperature is increased by 2 degreesC, what is the final pressure of the gas?
(P1/T1) = (P2/T2)
T must be in kelvin.
i need answer right away
To solve this problem, we can use the combined gas law formula, which relates the initial and final conditions of the gas:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure (what we want to find)
V2 = final volume (since it is held constant, it will be the same as the initial volume)
T2 = final temperature
Let's plug in the known values into the formula:
P1 = 742 mmHg
V1 = 5.00 L
T1 = 27 degrees Celsius
We need to convert the temperatures to Kelvin because the gas law requires temperature in Kelvin:
T1 (Kelvin) = T1 (Celsius) + 273.15
T1 = 27 + 273.15 = 300.15 K
Since V2 = V1 (volume is constant), we can rewrite the formula as:
(P1 * V1) / T1 = (P2 * V1) / T2
Now, we need to find the final temperature T2:
T2 = T1 + ΔT (change in temperature)
ΔT = 2 degrees Celsius
Again, we convert the temperature to Kelvin:
T2 (Kelvin) = T1 (Kelvin) + ΔT
T2 = 300.15 K + 2 = 302.15 K
Now, we can rearrange our formula to solve for the final pressure P2:
P2 = (P1 * T2) / T1
Plugging in the known values:
P2 = (742 mmHg * 302.15 K) / 300.15 K
Calculating this equation will give us the final answer for the pressure:
P2 = 747 mmHg (rounded to the nearest whole number)
Therefore, the final pressure of the gas is approximately 747 mmHg.