Answer:approximately 52.08 grams of ethyne are required to heat 1.50 kg of water from 20.0°C to 42.9°C
Explanation:To calculate the mass of ethyne required to heat 1.50 kg of water from 20.0°C to 42.9°C, you can use the following steps:Determine the heat energy required to raise the temperature of water.Use the heat energy to calculate the moles of ethyne needed.Calculate the mass of ethyne based on its molar mass.Let's break it down step by step:Step 1: Calculate the heat energy required to heat the water.The formula for calculating heat energy (q) is:q = m * C * ΔTWhere:
q = heat energy (in joules)
m = mass of the substance (in kilograms)
C = specific heat capacity (for water, C = 4.184 J/g°C or 4184 J/kg°C)
ΔT = change in temperature (in degrees Celsius)First, convert the mass of water to grams:
1.50 kg = 1500 gramsNow, calculate the heat energy:
q = 1500 g * 4.184 J/g°C * (42.9°C - 20.0°C)q ≈ 105,606 JStep 2: Calculate the moles of ethyne required.To find the moles of ethyne needed, you can use the balanced chemical equation provided. According to the equation:2 C2H2(g) + 5 O2(g) -> 4 CO2(g) + 2 H2O(g)The stoichiometric ratio of ethyne (C2H2) to water (H2O) is 2:2, which simplifies to 1:1. This means that 2 moles of C2H2 are required to produce 2 moles of H2O.Since 2 moles of H2O are produced when the temperature of water increases, the moles of ethyne required will be the same.Step 3: Calculate the mass of ethyne.Now, you need to calculate the mass of ethyne based on its molar mass. The molar mass of C2H2 (acetylene) is approximately 26.04 g/mol.Since 2 moles of C2H2 are required, the mass (m) of ethyne is:m = 2 moles * 26.04 g/mol ≈ 52.08 g