# Question #359b2

##### 1 Answer

#### Explanation:

In order to find the temperature of the gas, you need to use the **ideal gas law** equation, which looks like this

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

*universal gas constant*, usually given as

**absolute temperature** of the gas

The ideal gas law equation establishes a relationship between the pressure of the gas and the volume it occupies, on one hand, and the number of moles of gas and the *absolute temperature* of the gas, on the other.

It's important to keep in mind that you can only use the ideal gas law equation if the **units** given to you for pressure, volume, and temperature **match** those used in the expression of the universal gas constant.

In your case, all the units math those used for **absolute temperature** of the gas

#PV = nRT implies T = (PV)/(nR)#

Plug in your values to get

#T = (1.0 color(red)(cancel(color(black)("atm"))) * 85color(red)(cancel(color(black)("L"))))/(3.5color(red)(cancel(color(black)("moles"))) * 0.0821(color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/(color(red)(cancel(color(black)("mol"))) * "K")) = "295.81 K"#

In order to express this temperature in *degrees Celsius*, you must use the conversion factor

#color(purple)(|bar(ul(color(white)(a/a)color(black)(T["K"] = t[""^@"C"] + 273.15)color(white)(a/a)|)))#

In your case, you have

#t = "295.81 K" - 273.15 = 22.66^@"C"#

Rounded to two **sig figs**, the answer will be

#t = color(green)(|bar(ul(color(white)(a/a)23^@"C"color(white)(a/a)|)))#