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

`m=397.6gC_8H_(18)}`

Step-by-step 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=(-10,990kJ)/(2molC_8H_(18))=-5495(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=(Q)/(-\Delta H ) \\\\n=(19,126kJ)/(-(-5495(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)} *(114.22gC_8H_(18) )/(1molmolC_8H_(18)) } \\\\m=397.6gC_8H_(18)}`

Best regards!