# Question #a7aeb

##### 1 Answer

#### Explanation:

The first thing to recognize here is that no mention is made of *volume* and *number of moles of gas*, which means that you can safely assume that they are being **kept constant**.

Under these conditions, *pressure* and *temperature* have a **direct relationship** described by **Gay Lussac's Law**.

In simply terms, when temperature **increases**, pressure **increases** as well, and when pressure **decreases**, temperature **decreases** as well.

Mathematically, this is expressed as

#color(blue)(|bar(ul(color(white)(a/a)P_1/T_1 = P_2/T_2color(white)(a/a)|)))" "# , where

In your case, the temperature is said to go from *increase in temperature* could have only resulted from an *increase in pressure*, so right from the start you know that

#P_1 < "900 torr" -># .the pressure of the gasincreased

Rearrange the above equation to solve for

#P_1/T_1 = P_2/T_2 implies P_1 = T_1/T_2 * P_2#

Plug in your values to find

#P_1 = (300 color(red)(cancel(color(black)("K"))))/(450color(red)(cancel(color(black)("K")))) * "900 torr" = color(green)(|bar(ul(color(white)(a/a)color(black)("600 torr")color(white)(a/a)|)))#

As predicted, the pressure of the gas **increased** from

**SIDE NOTE** *The equation that describes Gay Lussac's Law can be derived from the ideal gas law equation*

#color(blue)(|bar(ul(color(white)(a/a)PV = nRTcolor(white)(a/a)|)))" "#

where

*universal gas constant*

**absolute temperature** of the gas

*When volume and number of moles are kept constant, you can rearrange the above equation to isolate the constants on one side of the equation*

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

*This tells you that under these conditions, pressure and temperature have a direct relationship, i.e. when one increases, the other must increase by the same factor in order to keep the*

*ratio constant*.

*Therefore, if you have a gas at* *and* *and then at a second state* *and* *you will have*

#P_1/T_1 = color(red)("constant") " "# and#" " P_2/T_2 = color(red)("constant")#

*which implies that*

#color(blue)(|bar(ul(color(white)(a/a)P_1/T_1 = P_2/T_2color(white)(a/a)|))) -># the equation that describesGay Lussac's Law