A strip of aluminium of mass 40.7g is dropped into a beaker of dilute hydrochloric acid. Calculate the work done (in J) on the surrounding atmosphere (1atm pressure, 26.1oC ) by the evolution of hydrogen in the subsequent reaction. State any assumptions you have made.
To calculate the work done on the surrounding atmosphere by the evolution of hydrogen, we need to consider the chemical reaction that occurs between aluminium and hydrochloric acid.
The chemical reaction involved is:
2Al + 6HCl → 2AlCl3 + 3H2
From the balanced equation, we can see that 2 moles of aluminium (Al) react with 6 moles of hydrochloric acid (HCl) to produce 3 moles of hydrogen gas (H2).
Assuming that the reaction goes to completion and that one mole of an ideal gas at standard temperature and pressure (STP) occupies 22.4 liters, the volume of hydrogen gas evolved can be calculated.
Given that the molar mass of aluminium is 26.98 g/mol and the mass of the aluminium strip is 40.7 g, we can calculate the number of moles of aluminium used in the reaction:
Moles of Al = Mass of Al / Molar Mass of Al
= 40.7 g / 26.98 g/mol
= 1.51 mol
Since the stoichiometric ratio between aluminium and hydrogen is 2:3, we can calculate the number of moles of hydrogen gas evolved:
Moles of H2 = (3/2) * Moles of Al
= (3/2) * 1.51 mol
= 2.26 mol
Now, we can calculate the volume of hydrogen gas evolved at STP:
Volume of H2 = Moles of H2 * 22.4 L/mol
= 2.26 mol * 22.4 L/mol
= 50.62 L
Next, we need to convert the volume of hydrogen gas from liters to cubic meters, as the SI unit of pressure is Pascal (Pa), and 1 m^3 = 1000 L:
Volume of H2 = 50.62 L * (1 m^3 / 1000 L)
= 0.05062 m^3
Since the work done on the surrounding atmosphere is given by the equation:
Work done (W) = Pressure (P) * Change in Volume (ΔV)
We need to calculate the change in volume of the surrounding atmosphere. Assuming the reaction occurs at constant temperature and pressure (1 atm), the change in volume is equal to the volume of the hydrogen gas evolved:
ΔV = 0.05062 m^3
Now, we can calculate the work done:
Work done (W) = Pressure (P) * Change in Volume (ΔV)
= 1 atm * 0.05062 m^3
= 0.05062 atm·m^3
To convert the work done from atm·m^3 to Joules (J), we can use the conversion factor:
1 atm·m^3 = 101.325 J
Therefore, the work done on the surrounding atmosphere by the evolution of hydrogen is:
Work done (W) = 0.05062 atm·m^3 * 101.325 J/atm·m^3
= 5.13 J
Assumptions made:
1. The reaction goes to completion.
2. The temperature remains constant during the reaction (26.1°C is not specified as the initial or final temperature).
3. The pressure remains constant at 1 atm.
4. The ideal gas law and stoichiometry are applicable.