# At 120.0°C, the pressure of a sample of nitrogen is 1.07 atm. What will the pressure be at 205°C, assuming constant volume?

##### 1 Answer

#### Answer:

#### Explanation:

The important thing to remember about a gas kept at **constant volume** is that its *pressure* and its *temperature* are **directly proportional**, assuming of course that the number of moles of gas are constant as well.

So, when volume and number of moles are kept constant, pressure and temperature have a **direct relationship** - this is known as Gay Lussac's Law.

Simply put, when temperature **increases**, pressure **increases**. Likewise, when temperature **decreases**, pressure **decreases** as well.

In your case, the temperature of the gas *increases* from *increase* as well.

Mathematically, Gay Lussac's Law is expressed like this

#color(blue)(P_1/T_1 = P_2/T_2)" "# , where

Now, it is **of the utmost importance** that you **do not** forget to convert the temperature from *degrees Celsius* to *Kelvin*!

In fact, the temperature **must** be expressed in Kelvin **regardless** of which gas law you're using.

So, plug in your values and solve for

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

#P_2 = ( (273.15 + 205)color(red)(cancel(color(black)("K"))))/((273.15 + 120.0)color(red)(cancel(color(black)("K")))) * "1.07 atm" = "1.4238 atm"#

Rounded to three sig figs, the number of sig figs you have for the second temperature of the gas, the answer will be

#P_2 = color(green)("1.42 atm")#