# Question #12c2c

##### 1 Answer

#### Explanation:

The idea here is that you're looking for the *mass* of the metal that will displace exactly **parts by mass** of elemental hydrogen,

The first thing that you need to do here is to use the **ideal gas law equation**

#color(blue)(ul(color(black)(PV = nRT)))#

Here

#P# is the pressure of the gas#V# is the volume it occupies#n# is the number of moles of gas present in the sample#R# is theuniversal gas constant, equal to#0.0821("atm L")/("mol K")# #T# is theabsolute temperatureof the gas

to find the **number of moles** of hydrogen gas, **NTP**, which are defined as a pressure of

Rearrange the equation to solve for

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

Plug in your values to find

#n = (1 color(red)(cancel(color(black)("atm"))) * 1.12color(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")))) * 293.15 color(red)(cancel(color(black)("K")))) = "0.04654 moles H"_2#

The number of moles of *elemental hydrogen* present in your sample will be equal to

#0.04654 color(red)(cancel(color(black)("moles H"_2))) * "2 moles H"/(1color(red)(cancel(color(black)("mole H"_2)))) ~~ "0.09308 moles H"#

Convert this to *grams* by using the molar mass of elemental hydrogen

#0.09308 color(red)(cancel(color(black)("moles H"))) * "1.008 g"/(1color(red)(cancel(color(black)("mole H")))) = "0.09382 g"#

Now, if

#1.008 color(red)(cancel(color(black)("g H"))) * "2.4 g metal"/(0.09382color(red)(cancel(color(black)("g H")))) = color(darkgreen)(ul(color(black)("26 g metal")))#

The answer is rounded to two **sig figs**, the number of significant figures you have for the mass of the metal.

**SIDE NOTE** *I suspect that the problem was designed with the old STP conditions in mind, i.e. a pressure of*

*and a temperature of*

*Under these conditions for pressure and temperature, the molar volume of an ideal gas is equal to*

*In this case, the number of moles of elemental hydrogen would come out to be equal to* *which would produce an equivalent mass of* *for the metal*.