# If measurements of a gas are 50L and 300 kilopascals and then the gas is measured a second time and found to be 75L, describe what had to happen to the pressure (if temperature remained constant). Include which law supports this observation?

Pressure had to decrease in order for the volume to increase.

The important thing to notice here is that temperature is being kept constant.

Assuming that the amount of gas you have remains constant as well, i.e. you don’t add or remove gas from the container, then you can use the equation to write

##P_1 * V_1 = n * R * T## ##->## for the first measurement

##P_2 * V_2 = n * R * T## ##->## for the second measurement

If you replace the product ##n * R * T##, which will be constant, in one of these two equations you’ll get

##P_1 * V_1 = P_2 * V_2##

This is the mathematical expression for , which states that pressure and volume have an inverse relationship when temperature and number of moles (amount of gas) are ket constant.

An inverse relationship means that if one increases, the other must decrease and vice versa.

Even before doing any calculations, you can use to predict what will happen to the pressure. If volume increased from 50 to 75 L, then the pressure musht have decreased proportionally.

You can confirm this by

##P_2 = V_1/V_2 * P_2##

##P_2 = (50cancel(“L”))/(75cancel(“L”)) * “300 kPa” = color(green)(“200 kPa”)##

The pressure indeed decreased, which corresponds to the increase in volume.

So, as a conclusion, when the temperature of the gas is constant, i.e. the average kinetic energy of the gas molecules remains unchanged, the volume the gas occupies can only increase if pressure decreases.

Likewise, the pressure of the gas can only decrease if the volume of the gas is increased.

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