At 36.4°C a sample of ammonia gas exerts a pressure of 6.8 atm. What is the pressure when the volume of the gas is reduced to one-fourth of the original value at the same temperature
P1V1 = P2V2
To answer this question, we can apply Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume if the temperature remains constant.
Boyle's Law equation: P₁ * V₁ = P₂ * V₂
Given:
- Initial pressure, P₁ = 6.8 atm
- Initial volume, V₁ = x (let's assume the initial volume as 'x')
- Final volume, V₂ = x/4 (one-fourth of the initial volume)
- Same temperature, so we don't need to consider it in the equation
Now, we can substitute the given values into the Boyle's Law equation and solve for the final pressure (P₂).
P₁ * V₁ = P₂ * V₂
6.8 * x = P₂ * (x/4)
First, let's simplify the equation:
6.8 * x = (P₂ * x) / 4
Next, we'll multiply both sides of the equation by 4 to eliminate the fraction:
(6.8 * 4) * x = P₂ * x
27.2 * x = P₂ * x
Since 'x' appears on both sides of the equation, we can cancel it out:
27.2 = P₂
Therefore, the pressure when the volume is reduced to one-fourth of the original value at the same temperature is 27.2 atm.