Question #5e940

1 Answer
Jan 29, 2016

Here's what I got.

Explanation:

Since your didn't provide enough information to allow for a direct answer, I'll try to take a more general approach and show you how to solve similar problems in the future.

Your tool of choice for any ideal gas problem is the ideal gas law equation. You can use it to derive all the other gas law equation.

color(blue)(PV = nRT)" ", where

P - the pressure of the gas
V - the volume it occupies
n - the number of moles of gas
R - the universal gas constant, usually given as 0.0821("atm" * "L")/("mol" * "K")
T - the absolute temperature of the gas, i.e. the temperature expressed in Kelvin.

Now, the problem starts like this

A sample of ammonia gas in a non-rigid container occupies a volume of "4.00 L" at a certain temperature and pressure**.

This tells you two important things

  • the number of moles of gas is probably constant
  • the volume of the gas is not constant**

We can now distinguish three possible scenarios

  • Pressure and temperature change

Let's say that the ammonia gas is initially kept at a pressure P_1 and a temperature T_1. If the number of moles of gas is indeed kept constant, you can rearrange the ideal gas law equation to get

PV = nRT implies (PV)/T = overbrace(n * R)^(color(green)("constant"))

This means that you can equate the initial state of the gas with a final state by writing

color(blue)((P_1V_1)/T_1 = (P_2V_2)/T_2) -> the combined gas law equation

This equation implies that both the temperature and the pressure of the gas change from T_1 and P_1, respectively, to T_2 and P_2.

To get the new volume of the gas, rearrange this equation to solve for V_2

V_2 = P_1/P_2 * T_2/T_1 * V_1

At this point, you would use the new values for pressure and temperature, P_2 and T_2, respectively, to find the new volume.

  • Pressure changes, but temperature remains constant

Once again, start from the ideal gas law equation. This time the pressure of the gas changes, but its temperature is kept constant.

PV = overbrace(n * R * T)^(color(green)("constant"))

You will thus have

color(blue)(P_1V_1 = P_2V_2 -> the equation for Boyle's Law

This time, the new volume of the gas will be

V_2 = P_1/P_2 * V_1

Finally, the third possible scenario

  • Pressure is kept constant, but temperature changes

Starting from the ideal gas law equation

PV = nRT implies V/T = overbrace((nR)/P)^(color(green)("constant"))

You will thus have

color(blue)(V_1/T_1 = V_2/T_2) -> the equation for Charles' Law

This time, the new volume of the gas will be

V_2 = T_2/T_1 * V_1

This is how you can figure out which gas law to use. Remember, the ideal gas law equation can be used as the starting point for all of them.