At 36.4°C a sample of ammonia gas exerts a pressure of 8.3 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
Make up a volume for V1 and take 1/4 of that for V2.
To solve this problem, you can apply Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume at constant temperature.
Boyle's Law can be expressed by the equation: P1 * V1 = P2 * V2, where P1 and V1 represent the initial pressure and volume, while P2 and V2 represent the final pressure and volume.
In this case, we know that the initial pressure (P1) is 8.3 atm and the final volume (V2) is one-fourth of the original volume (V1).
Let's substitute these values into the equation and solve for P2:
P1 * V1 = P2 * V2
8.3 atm * V1 = P2 * (1/4) * V1
Now, we can simplify the equation by canceling out V1 from both sides:
8.3 atm = P2 * (1/4)
To solve for P2, we need to isolate it on one side of the equation.
Divide both sides of the equation by (1/4):
8.3 atm / (1/4) = P2
To simplify, divide 8.3 atm by (1/4) by multiplying it by the reciprocal:
8.3 atm * (4/1) = P2
Now, multiply 8.3 atm by 4:
33.2 atm = P2
So, when the volume of the gas is reduced to one-fourth of its initial value while the temperature remains the same at 36.4°C, the pressure of the ammonia gas becomes 33.2 atm.