the pressure on 200 milliliters of a gas at constant temperature is changed from 50.65 kPa to 101.3 kPa. what is the new volume of the gas?
To find the new volume of the gas, we can use Boyle's Law, which states that the product of the initial pressure and volume is equal to the product of the final pressure and volume.
Boyle's Law formula: P1 * V1 = P2 * V2
Where:
P1 = Initial pressure (50.65 kPa)
V1 = Initial volume (200 ml)
P2 = Final pressure (101.3 kPa)
V2 = Final volume (to be calculated)
Let's plug in the given values into the formula:
50.65 kPa * 200 ml = 101.3 kPa * V2
Now, we can solve for V2:
(50.65 kPa * 200 ml) / 101.3 kPa = V2
Calculating the above expression:
(10,130 kPa * ml) / 101.3 kPa = V2
Simplifying:
(10000 ml) / 101.3 = V2
V2 ≈ 98.66 ml
Therefore, the new volume of the gas is approximately 98.66 ml.
To find the new volume of the gas, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when temperature is kept constant. The formula for Boyle's Law is:
P₁ × V₁ = P₂ × V₂
Where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume.
Given:
Initial pressure (P₁) = 50.65 kPa
Initial volume (V₁) = 200 mL
Final pressure (P₂) = 101.3 kPa
We need to find the final volume (V₂).
Rewriting the formula, we get:
V₂ = (P₁ × V₁) / P₂
Substituting the given values:
V₂ = (50.65 kPa × 200 mL) / 101.3 kPa
We need to convert milliliters (mL) to liters (L) to have consistent units. Since 1 L = 1000 mL, the conversion factor is 1/1000.
V₂ = (50.65 kPa × 200 mL × 1 L/1000 mL) / 101.3 kPa
Simplifying:
V₂ = (50.65 kPa × 0.2 L) / 101.3 kPa
The units of kilopascals (kPa) cancel out, leaving us with:
V₂ = (50.65 × 0.2) / 101.3 L
V₂ ≈ 0.100 L
Therefore, the new volume of the gas is approximately 0.100 liters.