Ideal Gas Law and Changes in P, V, T
You will encounter questions where a pressure, volume, or temperature change occurs. For example, if a solid-wall container is heated, the pressure inside will increase while the volume stays the same. If a balloon is heated, the internal pressure will stay the same but the volume will expand. Being able to predict how much the pressure, volume or temperature changes is an important skill. It is also possible (although more rare) for the number of moles to change, so we should be ready for that too. Here's my easy way to solve these types of problems. Always start with this equation:
and cancel out values that stay from the initial set of conditions to the second. Does the volume stay constant? Cancel out the V from each side. Does the temperature stay the same? Cancel out the T's. Note: R is ALWAYS constant....so always cancel it out! Then, plug your known values into the formula and solve for the unknown.
Q: An aerosol can has 2 atm of pressure on the inside at 298 K. The can will explode once the internal pressure is 10 atm. At what temperature will that happen?
A: Start with the equation from above:
What stays constant? Well, the volume of the can isn't likely to change ... when was the last time a metal can expanded like a balloon? Also, since no gas is entering or leaving the can, the number of moles inside stays constant too. So, once we cancel V, n and R rom the equation, we're left with:
You may remember this as one of the gas laws...Boyle's Law or Charles' Law or something. I never bothered to memorize those, because I always just use this method to find the right equation.
In any case, substitute the values we know and solve for the one that we don't...