The flame in a torch used to cut metal is produced by burning acetylene (C2H2) in pure oxygen. Assuming the combustion of 1 mole of acetylene releases 1251 kJ of heat, what mass of acetylene is needed to cut through a piece of steel if the process requires 95.5 * 104 kJ of heat?

19.8 kg of C₂H₂ is needed

Explanation:

We solve this by a rule of three:

If 1251 kJ of heat are relased in the combustion of 1 mol of acetylene

95.5*10⁴ kJ of heat may be released by the combustion of

(95.5*10⁴ kJ. 1) / 1251kJ = 763.4 moles of C₂H₂

Let's convert the moles to mass → 763.4 mol. 26 g/1 mol = 19848 g

If we convert the mass from g to kg → 19848 g. 1kg / 1000g = 19.8 kg

We need 19.88 kg of acetylene

Explanation:

Step 1: Data given

The combustion of 1 mole of acetylene releases 1251 kJ of heat

Step 2: Calculate moles acetylene needed

If we burn 1 mol, there is 1251 kJ released

If we burn x moles there is 95.5 * 10^4 kJ

x = 95.5 * 10^4 / 1251

x = 763.4

If we burn 763.4 moles there is 95.5 * 10^4 kJ released

Step 3: Calculate mass acetylene

Mass acetylene = moles * molar mass

Mass acetylene = 763.4 moles * 26.04 g/mol

Mass acetylene = 19878.9 grams = 19.88 kg

We need 19.88 kg of acetylene