The octane number of a fuel whose performance is the same as that of a mixture of 55 g of 2,2,4- trimethly pentane and 45 g of n-heptane is ?

The octane number of a fuel is a measure of its ability to resist "knocking" or detonation during combustion in an internal combustion engine. A fuel with a higher octane number is more resistant to knocking, and therefore is typically used in high-performance engines that require high compression ratios or high operating temperatures. The octane number of a fuel is determined by comparing its performance to a mixture of 2,2,4-trimethylpentane (iso-octane) and n-heptane. This mixture is assigned an octane rating of 100 because it has very high resistance to knocking. Fuels that perform as well as the 2,2,4-trimethylpentane/n-heptane mixture are assigned higher octane numbers, while fuels that perform worse are assigned lower numbers. In this problem, we are given that the performance of the fuel is the same as a mixture of 55 g of 2,2,4-trimethylpentane and 45 g of n-heptane. We can use this information to determine the octane number of the fuel by comparing its performance to the 55/45 mixture. The octane number of the fuel can be calculated as follows: octane number = (volume percentage of iso-octane in the mixture) x 100 To find the volume percentage of iso-octane in the mixture, we need to calculate the moles of each component in the mixture, using their respective molecular weights: moles of iso-octane = 55 g / 114.23 g/mol = 0.481 moles moles of n-heptane = 45 g / 100.21 g/mol = 0.449 moles The volume percentage of iso-octane in the mixture can be calculated using their respective densities and molecular weights: volume percentage of iso-octane = (0.481 mol x 114.23 g/mol) / (0.481 mol x 114.23 g/mol + 0.449 mol x 100.21 g/mol) x 100% = 55.96% Therefore, the octane number of the fuel is approximately 56, which is closest to option (A) 45. Note that the octane number of a fuel is typically reported as an integer, so the actual octane number of the fuel in this problem would likely be rounded down to 55.