Final answer:
To find out how many grams of carbon are needed to react with 6.87 moles of SO2, we use the stoichiometric ratio of carbon to sulfur dioxide from the balanced equation (5:2). The calculation gives us 17.175 moles of carbon, which we then convert to grams using the molar mass of carbon, resulting in 206 grams of carbon required.
Step-by-step explanation:
To determine how many grams of carbon are needed to react with 6.87 moles of sulfur dioxide (SO2) according to the equation 5C + 2SO2 → CS2 + 4CO, we need to perform stoichiometric calculations.
First, we note the molar ratio of carbon to sulfur dioxide is 5:2 from the balanced chemical equation, meaning 5 moles of carbon react with 2 moles of sulfur dioxide. To calculate the moles of carbon needed for 6.87 moles of SO2, we use this ratio:
Moles of C required = (6.87 moles SO2) x (5 moles C / 2 moles SO2)
= 17.175 moles of C
Next, we convert the moles of carbon to grams using the molar mass of carbon, which is 12.01 g/mol.
Mass of C required = (17.175 moles of C) x (12.01 g/mol)
= 206.29175 g of C
Our final answer is expressed to three significant figures, thus we need 206 g of carbon to react with 6.87 moles of sulfur dioxide.