Assume that you have a cylinder with a movable piston. What would happen to the gas pressure inside the cylinder if you were to do the following? (b) Reduce the amount of gas by one-third while holding the temperature and volume constant

Video transcript

Hello everyone today. We have the following problem. Suppose the gas samples continued in the cylinder with a movable piston, the amount of gas and the container is doubled at constant temperature and volume, identify the change in pressure of the gas. So first it's important to recall our ideal gas law which states that the pressure times the volume is equal to the amount of moles that we have times the gas constant R times R. T, which is temperature. And so essentially we want to solve for our variables of gas and our valuables are variable with pressure. And so we want to rearrange this equation to get this in terms of pressure over volume. And so we can do that by having our gas constant times our temperature or the volume is equal to our pressure over moles. And so we can take this a step further that we can write this in terms of our initial pressure over our initial moles is equal to our final pressure over our final moles. And so third, what we want to do is we want to isolate the variable for our final pressure since we want to find a change in the pressure. And so through some algebra we get that the final pressure is equal to the initial pressure times the final amount of molds that we have over the initial amount of molds that we have. And according to our question stem the amount of gas was doubled. So our final number of moles is going to be equal to twice the initial amount of moles that we had. And so we're going to essentially plug this in to our equation that we had in step three for our final number of moles. And so that's going to be our step five. So we're going to have our final pressure is equal to our initial pressure times two times our initial amount of moles over our initial amount of moles. So what we can do next is cross out our initial moles, since the variables are the same in the numerator and denominator, and we're dividing it and then we can end up with the answer that our final pressure is equal to two times our initial pressure. So essentially this gives us answer choice B as the pressure would be doubled and that is what this two represents in front of the initial pressure. And with that we've answered the question overall. I hope this helped until next time.