Final answer:
To calculate the molar composition of the product gas, we need to find the moles of each component. The molar composition is 42.585 moles of ethylene, 85.17 moles of methane, and the balance inerts. The selectivity of ethylene to methane production is 0.500.
Step-by-step explanation:
Yield is defined as the ratio of the amount of desired product formed to the maximum amount of product that could be formed, expressed as a fraction or a percentage. Selectivity refers to the ratio of the amount of a specific desired product to the amount of a competing product.
To calculate the molar composition of the product gas, we need to first find the moles of each component. Given that the fractional conversion of ethane is 0.501, we can calculate the moles of ethane converted using the initial moles of ethane in the feed and the fractional conversion. Since the feed contains 85.0 mole% ethane, and assuming a total of 100 moles, there are 85 moles of ethane. Therefore, the moles of ethane converted is 85 * 0.501 = 42.585 moles. Since 1 mole of ethane produces 1 mole of ethylene, the moles of ethylene produced is also 42.585 moles.
To calculate the moles of methane produced, we need to use the balance equation C2H6 + H2 -> 2CH4. Since 2 moles of methane are produced per mole of ethane converted, the moles of methane produced is 2 * 42.585 = 85.17 moles. The molar composition of the product gas is therefore as follows: 42.585 moles of ethylene, 85.17 moles of methane, and the balance inerts.
To calculate the selectivity of ethylene to methane production, we need to find the ratio of the moles of ethylene produced to the moles of methane produced. This is given by the equation: Selectivity = (moles of ethylene produced) / (moles of methane produced). Substituting the values calculated above, the selectivity of ethylene to methane production is 42.585 / 85.17 = 0.500.