Question

Question #c5367

Answer 1

The volume of hydrogen would be 7.47 L.

Explanation:

There are four steps involved in this problem:

1. Write the balanced equation for the reaction.
2. Use the molar mass of `"Mg"` to calculate the moles of `"Mg"`.
3. Use the molar ratio of `"Mg":"H"_2` from the balanced equation to calculate the moles of `"H"_2`.
4. Use the Ideal Gas Law to calculate the volume of `"H"_2` at STP.

Step 1. Write the balanced chemical equation.

`"Mg" + "2HCl" → "MgCl"_2 + "H"_2`

Step 2. Calculate the moles of `"Mg"`.

`"Moles of Mg" = 8.0 color(red)(cancel(color(black)("g Mg"))) × "1 mol Mg"/(24.30 color(red)(cancel(color(black)("g Mg")))) = "0.329 mol Mg"`

Step 3. Calculate the moles of `"H"_2`

`"Moles of H"_2 = 0.329 color(red)(cancel(color(black)("mol Mg"))) × "1 mol H"_2/(1 color(red)(cancel(color(black)("mol Mg")))) = "0.329 mol H"_2`

Step 4. Calculate the volume of `"H"_2`

The Ideal Gas Law is

`color(blue)(bar(ul(|color(white)(a/a)PV = nRTcolor(white)(a/a)|)))" "`

We can rearrange this equation to get

`V = (nRT)/P`

STP is defined as 1 bar and 0 °C, so

`n = "0.329 mol"`
`R = "0.083 14 bar·L·K"^"-1""mol"^"-1"`
`T = "0 °C" = "273.15 K"`
`P = "1 bar"`

∴ `V = (0.329 color(red)(cancel(color(black)("mol"))) × "0.083 14" color(red)(cancel(color(black)("bar")))·"L"·color(red)(cancel(color(black)("K"^"-1""mol"^"-1"))) × 273.15 color(red)(cancel(color(black)("K"))))/(1 color(red)(cancel(color(black)("bar")))) = "7.47 L"`