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Chapter 3: Problem 71

The complete combustion of octane, \(\mathrm{C}_{8} \mathrm{H}_{18}\), produces \(5470 \mathrm{~kJ}\) of heat. Calculate how many grams of octane is required to produce \(20,000 \mathrm{~kJ}\) of heat.

Short Answer

Expert verified
Approximately 3.66 grams of octane is required to produce 20,000 kJ of heat.

Step by step solution

01

Write down the known information

We are given the following pieces of information: 1. Heat produced by complete combustion of octane: 5470 kJ 2. We need to calculate the grams of octane required to produce 20,000 kJ of heat.
02

Setting up the proportion

Since we know the heat produced by the complete combustion of octane, we can set up a proportion that relates the heat produced (in kJ) to the grams of octane required. Let x be the grams of octane required to produce 20,000 kJ of heat. Then, we can set up the following proportion: \(\frac{Heat \, produced \, by \, octane}{Grams \, of \, octane} = \frac{Heat \, needed}{Grams \, of \, octane \, needed}\)
03

Plugging in the known values

Now we will plug in the known values into the proportion: \(\frac{5470 \, kJ}{1 \, g \, of \, C_{8}H_{18}} = \frac{20,000 \, kJ}{x \, g \, of \, C_{8}H_{18}}\)
04

Solve for x

We can now solve for x, which represents the grams of octane required to produce 20,000 kJ of heat. 1. Cross-multiply: \(5470 \, kJ \times x = 20,000 \, kJ \times 1 \, g\) 2. Simplify: \(5470x = 20,000\) 3. Divide by 5470: \(x = \frac{20,000}{5470}\) 4. Calculate the result: \(x ≈ 3.66\)
05

Conclusion

The grams of octane required to produce 20,000 kJ of heat is approximately 3.66 grams.

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Most popular questions from this chapter

A chemical plant uses electrical energy to decompose aqueous solutions of \(\mathrm{NaCl}\) to give \(\mathrm{Cl}_{2}, \mathrm{H}_{2},\) and \(\mathrm{NaOH}\) : $2 \mathrm{NaCl}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{NaOH}(a q)+\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g)$ If the plant produces \(1.5 \times 10^{6} \mathrm{~kg}\) ( 1500 metric tons) of \(\mathrm{Cl}_{2}\) daily, estimate the quantities of \(\mathrm{H}_{2}\) and \(\mathrm{NaOH}\) produced.

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A mixture of \(\mathrm{N}_{2}(g)\) and \(\mathrm{H}_{2}(g)\) reacts in a closed container to form ammonia, \(\mathrm{NH}_{3}(g)\). The reaction ceases before either reactant has been totally consumed. At this stage $3.0 \mathrm{~mol} \mathrm{~N}_{2}, 3.0 \mathrm{~mol} \mathrm{H}_{2}\(, and \)3.0 \mathrm{~mol} \mathrm{NH}_{3}\( are present. How many moles of \)\mathrm{N}_{2}$ and \(\mathrm{H}_{2}\) were present originally?

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