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

##### 1 Answer
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 $\text{Co}$.

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