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 #"H"_2#.
  3. Use the molar ratio of #"Co":"H"_2# from the balanced equation to calculate the moles of #"Co"#.
  4. Use the molar mass of #"Co"# to calculate the mass of #"Co"#.

Let's get started.

Step 1. Write the balanced chemical equation.

#"Co"+ "2HCl" → "CoCl"_2 + "H"_2#

Step 2. Calculate the moles of #"H"_2#.

The Ideal Gas Law is

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

#P = "1 bar"#
#V = "0.0250 L"#
#R = "0.083 14 bar·L·K"^"-1""mol"^"-1"#
#T = 0^@"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 #"Co"#

#"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 #"Co"#.

#"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"#