The combustion of 1.00 g of gasoline releases 11100 cal of heat energy. Determine the number of megajoules (MJ) released when 1.75 gallons of gasoline is burned. (Density of gasoline = 0.740 g/mL)
1.00g = 11100 cal
how much grams in gallons???..how much joules in calories???...knowing these can lead you to your answer...
To solve this problem, we need to follow a few steps.
Step 1: Convert volume from gallons to milliliters.
1 gallon is equal to 3.78541 liters, and 1 liter is equal to 1000 milliliters. Therefore, we can convert 1.75 gallons to milliliters by multiplying by the conversion factors:
1.75 gallons * 3.78541 liters/gallon * 1000 ml/liter = 6604.47 milliliters.
Step 2: Calculate the mass of the gasoline used.
Given that the density of gasoline is 0.740 g/mL, we can calculate the mass of the gasoline used by multiplying the volume by the density:
6604.47 ml * 0.740 g/ml = 4878.96 g.
Step 3: Convert energy from calories to megajoules.
We are given that the combustion of 1.00 g of gasoline releases 11100 calories. We need to convert this energy to megajoules (MJ). There are 4.184 joules in a calorie, and 1 megajoule is equal to 1,000,000 joules. So, to convert from calories to megajoules, we can use:
11100 calories * (4.184 joules/calorie) / (1,000,000 joules/MJ) = 0.0464 MJ.
Step 4: Calculate the energy released when 1.75 gallons of gasoline is burned.
Now that we have the mass of the gasoline used and the energy released per gram, we can calculate the total energy released by multiplying the mass by the energy per gram:
4878.96 g * 0.0464 MJ/g = 226.35 MJ.
Therefore, when 1.75 gallons of gasoline is burned, it releases approximately 226.35 megajoules of heat energy.