Question

Question #12c2c

Answer 1

`"26 g"`

Explanation:

The idea here is that you're looking for the mass of the metal that will displace exactly `1.008` parts by mass of elemental hydrogen, `"H"`.

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 the universal gas constant, equal to `0.0821("atm L")/("mol K")`
• `T` is the absolute temperature of the gas

to find the number of moles of hydrogen gas, `"H"_2`, present in your sample under normal conditions for pressure and temperature, i.e. at NTP, which are defined as a pressure of `"1 atm"` and a temperature of `20^@"C = 293.15 K"`,

Rearrange the equation to solve for `n`

`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 `"0.09382 g"` of hydrogen were displaced by `"2.4 g"` of metal, it follows that `"1.008 g"` of hydrogen will be displaced by

`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.

`color(white)(a)`
SIDE NOTE I suspect that the problem was designed with the old STP conditions in mind, i.e. a pressure of `"1 atm"` and a temperature of `0^@"C"`.

Under these conditions for pressure and temperature, the molar volume of an ideal gas is equal to `"22.4 L"`.

In this case, the number of moles of elemental hydrogen would come out to be equal to `0.100`, which would produce an equivalent mass of `"24 g"` for the metal.