How many grams of cobalt must react with an excess volume of hydrochloric acid to produce 25.0 mL of hydrogen gas?

Mar 27, 2016

How many grams of cobalt must react with an excess volume of hydrochloric acid to produce 25.0 mL of hydrogen gas?

The reaction requires 0.0649 g of cobalt.

We aren’t given the pressure or the volume, so let's assume STP (1 bar and 0 °C).

There are four steps involved in this problem:

1. Write the balanced equation for the reaction.
2. Use the Ideal Gas Law to calculate the moles of ${\text{H}}_{2}$.
3. Use the molar ratio of ${\text{Co":"H}}_{2}$ from the balanced equation to calculate the moles of $\text{Co}$.
4. Use the molar mass of $\text{Co}$ to calculate the mass of $\text{Co}$.

Let's get started.

Step 1. Write the balanced chemical equation.

${\text{Co"+ "2HCl" → "CoCl"_2 + "H}}_{2}$

Step 2. Calculate the moles of ${\text{H}}_{2}$.

The Ideal Gas Law is

color(blue)(|bar(ul(PV = nRT)|)

$P = \text{1 bar}$
$V = \text{0.0250 L}$
$R = \text{0.083 14 bar·L·K"^"-1""mol"^"-1}$
$T = {0}^{\circ} \text{C = 273.15 K}$

We can rearrange the Ideal Gas Law to get:

n = (PV)/(RT) = (1 color(red)(cancel(color(black)("bar"))) × 0.0250 color(red)(cancel(color(black)("L"))))/("0.083 14"color(red)(cancel(color(black)(" bar·L·K"^"-1")))"mol"^"-1" × 273.15 color(red)(cancel(color(black)("K")))) = "0.001 101 mol"

2. Calculate the moles of $\text{Co}$

$\text{moles of Co" = "0.001 101" color(red)(cancel(color(black)("mol H"_2))) × "1 mol Co"/(1 color(red)(cancel(color(black)("mol H"_2)))) = "0.001 101 mol Co}$

3. Calculate the mass of $\text{Co}$.

$\text{mass of Na" = "0.001 101" color(red)(cancel(color(black)("mol Co"))) × "58.93 g Co"/(1 color(red)(cancel(color(black)("mol Co")))) = "0.0649 g Co}$