A gas sample has a volume of 150ml when the pressure is 175kPa. If the temperature and amount of gas remains constant, what volume will the gas sample occupy at a pressure of 120 kPa
To solve this problem, we can use the combined gas law, which relates the initial and final conditions of a gas sample when the temperature and amount of gas remain constant.
The combined gas law equation is:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure (which we want to find)
V2 = final volume (which we want to find)
T2 = final temperature (which is given to be the same as the initial temperature)
Now, let's substitute the given values:
P1 = 175 kPa
V1 = 150 ml
T1 = T2 (temperature remains constant)
P2 = 120 kPa (final pressure we want to find)
V2 = ? (final volume we want to find)
We can rearrange the equation to solve for V2:
V2 = (P1 * V1 * T2) / (P2 * T1)
Since T1 = T2, we can simplify the equation to:
V2 = (P1 * V1) / P2
Now we can substitute the values:
V2 = (175 kPa * 150 ml) / 120 kPa
To solve for V2, we need to multiply the pressure and volume, then divide by the new pressure:
V2 = (26250 kPa * ml) / 120 kPa
Now, we cancel out the units:
V2 = 218.75 ml
Therefore, the gas sample will occupy a volume of 218.75 ml at a pressure of 120 kPa.