Final answer:
To find the mass of solid carbon needed to produce 15.0 L of CO at STP, calculate the moles of CO using its volume and the molar volume at STP, then use the molar mass of carbon to convert moles to grams. The result is 8.04 g of C.
Step-by-step explanation:
To calculate the mass in grams of solid carbon that must react to produce 15.0 L of CO at Standard Temperature and Pressure (STP), we need to use the concept of molar volume of a gas at STP. At STP, one mole of any gas occupies 22.414 liters. Since CO (carbon monoxide) and CO2 (carbon dioxide) both contain one carbon atom per molecule, the chemical equations involving their formation from carbon will have the same molar ratio between carbon and the gas.
First, we calculate the number of moles of CO that can be produced from 15.0 L CO at STP:
Number of moles (CO) = Volume of CO / Molar volume at STP
Number of moles (CO) = 15.0 L / 22.414 L mol-1
Number of moles (CO) = 0.669 moles CO
Now, since one mole of CO is produced from one mole of C, the number of moles of carbon needed is the same as the moles of CO, which is 0.669 moles of C.
Using the molar mass of carbon which is 12.011 g/mol, we can find the mass of carbon required:
Mass of carbon (C) = Number of moles (C) × Molar mass (C)
Mass of carbon (C) = 0.669 moles × 12.011 g/mol
Mass of carbon (C) = 8.04 g