# Question #b51d7

##### 1 Answer

#### Explanation:

In order to be able to determine the identity of the gas, you must figure out its **molar mass**.

Since you know the *mass* of the sample, you can use the **ideal gas law** equation to find the *number of moles* present in the sample. Dividing these two values will give you the molar mass of the gas.

So, the ideal gas law equation looks like this

#color(blue)(PV = nRT)" "# , where

*number of moles* of gas

*universal gas constant*, usually given as

**absolute temperature** of the gas

Now, you need to pay attention to the **units** used in the expression of the ideal gas constant and make sure that your units **match** those units.

You need to have the pressure expressed in *atm*, the volume in *liters*, and the temperature in *Kelvin*, so use the conversion factors

#"1 L" = 10^3"mL"#

#"1 atm " = "760 torr"#

Rearrange the ideal gas law equation to solve for

#PV = nRT implies n = (PV)/(RT)#

#n = (943/760 color(red)(cancel(color(black)("atm"))) * 275 * 10^(-3)color(red)(cancel(color(black)("L"))))/(0.0821(color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/("mol" * color(red)(cancel(color(black)("K")))) * (273.15 + 25.5)color(red)(cancel(color(black)("K"))))#

#n = "0.01392 moles"#

The **molar mass** of the gas will tell you the mass of **one mole** of the gas. Since you know that *one mole* will have a mass of

#1color(red)(cancel(color(black)("mole"))) * "2.22 g"/(0.01392color(red)(cancel(color(black)("moles")))) = "159.5 g"#

This means that the molar mass of the gas is equal to

The only gas on your list that comes close to having this molar mass is *bromine*,

All the other options have significantly smaller molar masses, so bromine will be your answer.