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# 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**.