Combustion of hydrocarbons such as methane (CH4) produces carbon dioxide, a "greenhouse gas." Greenhouse gases in the Earth's atmosphere can trap the Sun's heat, raising the average temperature of the Earth. For this reason there has been a great deal of international discussion about whether to regulate the production of carbon dioxide.1. Write a balanced chemical equation, including physical state symbols, for the combustion of gaseous methane into gaseous carbon dioxide and gaseous water.2. Suppose 0.350kg of methane are burned in air at a pressure of exactly 1atm and a temperature of 12.0°C. Calculate the volume of carbon dioxide gas that is produced. Be sure your answer has the correct number of significant digits.L
Question
Combustion of hydrocarbons such as methane (CH4) produces carbon dioxide, a "greenhouse gas." Greenhouse gases in the Earth's atmosphere can trap the Sun's heat, raising the average temperature of the Earth. For this reason there has been a great deal of international discussion about whether to regulate the production of carbon dioxide.1. Write a balanced chemical equation, including physical state symbols, for the combustion of gaseous methane into gaseous carbon dioxide and gaseous water.2. Suppose 0.350kg of methane are burned in air at a pressure of exactly 1atm and a temperature of 12.0°C. Calculate the volume of carbon dioxide gas that is produced. Be sure your answer has the correct number of significant digits.L
Solution
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The balanced chemical equation for the combustion of gaseous methane into gaseous carbon dioxide and gaseous water is:
CH4(g) + 2O2(g) -> CO2(g) + 2H2O(g)
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To calculate the volume of carbon dioxide gas that is produced, we first need to know the number of moles of methane that are burned. The molar mass of methane (CH4) is approximately 16.04 g/mol. So, 0.350 kg or 350 g of methane is:
350 g / 16.04 g/mol = 21.82 mol
From the balanced chemical equation, we know that one mole of methane produces one mole of carbon dioxide. Therefore, the number of moles of carbon dioxide produced is also 21.82 mol.
The volume of one mole of gas at standard temperature and pressure (STP) is 22.4 L. However, the problem states that the temperature is 12.0°C, not 0°C (which is the temperature at STP). We need to convert this temperature to Kelvin by adding 273.15:
12.0°C + 273.15 = 285.15 K
We can then use the ideal gas law (PV=nRT) to calculate the volume (V) of the carbon dioxide gas. In this equation, P is the pressure (1 atm), n is the number of moles (21.82 mol), R is the ideal gas constant (0.0821 L·atm/K·mol), and T is the temperature in Kelvin (285.15 K):
V = nRT / P V = (21.82 mol)(0.0821 L·atm/K·mol)(285.15 K) / 1 atm V = 534.5 L
So, the volume of carbon dioxide gas produced is 534.5 L. This answer has four significant digits because the number with the least number of significant digits in the problem is the temperature (12.0°C), which has three significant digits.
Similar Questions
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Air contains 79% N2 and 21% O2 on a molar basis. Methane (CH4) is burned with 50% excess air than required stoichiometrically. Assuming complete combustion of methane, the molar percentage of N2 in the products is::
Which greenhouse gas is produced by the combustion of fossil fuels?1 markMethaneNitrous OxideWater VaporCarbon dioxide
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