Acetylene (C2H2) can be produced through a chemical reaction between water (H2O) and calcium carbide (CaC2): CaC2 (s) + 2H2O(l) → C2H2 (g) + Ca(OH)2 (s),where (s) and (l) indicate whether the substance is solid or liquid. A cave explorer considers using an acetylene torch,known to consume this gas

Question

Acetylene [latex] (C_2H_2) [/latex] can be produced through a chemical reaction between water [latex](H_2O) [/latex] and calcium carbide [latex](CaC_2) [/latex]:

[latex] CaC_2 (s) + 2 H_2O(l) → C_2H_2 (g) + Ca(OH)_2 (s) [/latex].

where (s) and (l) indicate whether the substance is solid or liquid. A cave explorer considers using an acetylene torch, known to consume this gas at a volume rate of [latex]\dot {V}[/latex] (at standard conditions of temperature and pressure). As the expedition is due to last a time t, find the amount of calcium carbide that the explorer would need if he chose this type of light source. Determine the amount of water used by this torch during this time.

Numerical application:

[latex] T = 0°C, p = 10^5 atm, \dot {V} [/latex]= 10 l/h and t = 8 h.

Accepted Answer

Acetylene can be considered as an ideal gas. Thus, at standard conditions of pressure and temperature, the number of moles of [latex] C_2H_2[/latex] needed for this exploration is,

[latex] N_{C _2 H_ 2} = \frac{ pV }{ RT } = \frac{ p\dot {V} t}{ RT } [/latex]= 3.52 mol.

Since the stoichiometric coefficients of acetylene and calcium carbide are equal and opposite, i.e. [latex]ν_{C _2 H _2} = −ν_{CaC_2}[/latex] = 1, it means that [latex]N_{CaC_2} = N_{C_2H_2}[/latex] = 3.52 mol of calcium carbide are consumed and produce 3.52 mol of acetylene. The mass [latex]m_{CaC_2}[/latex] of calcium carbide is the product of the number of moles [latex]N_{C_2H_2}[/latex] and the molar mass [latex]M_{CaC_2}[/latex] = 64 g,

[latex] m_{CaC_2} = N_{CaC_2} M_{CaC_2} = N_{C_2H_2} M_{CaC_2} [/latex] = 225 g.

Since the stoichiometric coefficient of water is twice the opposite stoichiometric coefficient of acetylene, i.e. [latex]ν_{H_2O} = −2 ν_{C_2H_2} = 2[/latex], it means that [latex]N_{H_2O} = 2 N_{C_2H_2}[/latex] = 7.05 mol of water are consumed in order to produce 3.52 mol of acetylene. The mass [latex]m_{H_2O}[/latex] of water is the product of the number of moles [latex]N_{H_2O}[/latex] and the molar mass [latex]M_{H_2O}[/latex] = 18 g,

[latex] m_{H_2O} = N_{H_2O} M_{H_2O} = 2 N_{C_2H_2} M_{H_2O}[/latex] = 127 g.

Question 8.2: Acetylene (C2H2) can be produced through a chemical reaction...

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