Question

The reaction of magnesium with hydrochloric acid at 30 °C and 817.36 mmHg produced 4.03 L of hydrogen that was collected over water. The vapour pressure of water at 30 °C is 33.4 mmHg. How many moles of hydrogen were formed?

Answer 1

`1.67\times10^-1color(white)(l)"mol"`

Explanation:

The Reaction:

`Mg(s)+2HCl(aq)\rightarrowMgCl_2(aq)+H_2(g)`

Data given:

Pressure `P="817.36 mmHg"`
Volume `V="4.03 L"`
Temperature `T="303 K"`

Work :

`P_"total" = P_"H₂" + P_"H₂O"`

At 303 K, `P_"H₂O" = "33.4 mmHg"`

∴ `P_"H₂" = P_"total" - P_"H₂O" = "817.36 mmHg" - "33.4 mmHg" = "783.96 mmHg" = "1.0315 atm"`

Apply the Ideal Gas Law `PV=nRT` to get `n = \frac(PV)(RT)`

The constant `R = "0.0821 L·atm·K"^"-1""mol"^"-1"`

`\frac("1.0315 atm"\times"4.03 L")("0.0821 L·atm·K"^"-1""mol"^"-1"\times"303 K") = 1.67\times10^-1color(white)(l)"mol"`