A volume (54.2 L) of gas at 1150 mmHg is subjected to a new pressure of 3450 mmHg, at constant temperature. What volume in liters (L) does the gas now occupy
Volume 1 = 54.2 L
Pressure 1 = 1150 mmHg
Volume 2 = ?
Pressure 2 = 3450 mmHg
54.2 L * (1150/3450) = 18 L
1150/3450 because volume should get smaller since pressure is increasing
OK BUT why did you throw away a digit. You have three places in 54.2 but only two in the answer.
To find the new volume of the gas, we can use the combined gas law equation:
(P₁ * V₁) / T₁ = (P₂ * V₂) / T₂
Where:
P₁ = initial pressure (1150 mmHg)
V₁ = initial volume (54.2 L)
T₁ = initial temperature (constant)
P₂ = new pressure (3450 mmHg)
V₂ = new volume (to be calculated)
T₂ = initial temperature (constant)
Since the temperature remains constant, we can simplify the equation to:
(P₁ * V₁) = (P₂ * V₂)
Now, let's plug in the values we have:
(1150 mmHg) * (54.2 L) = (3450 mmHg) * V₂
To solve for V₂, divide both sides of the equation by 3450 mmHg:
V₂ = (1150 mmHg * 54.2 L) / 3450 mmHg
Now, let's calculate the value:
V₂ = (62,330 mmHg * L) / 3450 mmHg = 18.06 L (rounded to two decimal places)
Therefore, the gas now occupies a volume of approximately 18.06 liters (L).