Question

My sporty mini van needs 19,126 kJ of energy in order to pass a fast moving street sweeper on the road. Using the following equation, determine how many grams of gasoline (C8H18) will be used up in order to make this happen. 2 C8H18 + 25 O2 --> 16 CO2 + 18 H2O \DeltaΔH = -10,990 kJ

Answer 1

Answer:

$m=397.6gC_8H_{18}}$

Explanation:

Hello there!

In this case, according to the given chemical reaction, we can set up the heat of reaction per mole of gasoline as shown below:

$\Delta H=\frac{-10,990kJ}{2molC_8H_{18}}=-5495\frac{kJ}{molC_8H_{18}}$

Now, since the total heat is obtained by multiplying the moles and heat of reaction, we can calculate the moles as shown below:

$n=\frac{Q}{-\Delta H } \\\\n=\frac{19,126kJ}{-(-5495\frac{kJ}{molC_8H_{18}} )} \\\\n=3.48molC_8H_{18}}$

Finally, since the molar mass of gasoline is 114.22 g/mol, we can easily calculate the mass as follows:

$m=3.48molC_8H_{18}} *\frac{114.22gC_8H_{18} }{1molmolC_8H_{18}} } \\\\m=397.6gC_8H_{18}}$

Best regards!