Problem 19 - Chemistry: The Central Science

Question

What is the octane number of a mixture that is \(35 \%\) heptane and \(65 \%\) isooctane?

Step-by-Step Solution

Answer

The octane number of the mixture containing 35% heptane and 65% isooctane can be calculated using a weighted average formula: Octane number of the mixture = (0.35 × 0) + (0.65 × 100). The result is an octane number of 65 for the mixture.

Step 1: Write down the formula for calculating the octane number of the mixture

The octane number of the mixture can be calculated as a weighted average of the octane numbers of its components (heptane and isooctane), using their respective percentages as weights. The formula is: Octane number of the mixture = (percentage of heptane × octane number of heptane) + (percentage of isooctane × octane number of isooctane)]

Step 2: Substitute the given percentages and octane numbers

Now, let's substitute the given values into the formula. As mentioned earlier, the octane numbers of pure heptane and isooctane are 0 and 100, respectively. The percentage of heptane and isooctane in the mixture are 35% and 65%, respectively. Octane number of the mixture = (0.35 × 0) + (0.65 × 100)

Step 3: Calculate the octane number of the mixture

Now, we just need to do the calculations: Octane number of the mixture = (0) + (65) Octane number of the mixture = 65 So, the octane number of the mixture is 65.