The balanced equation below shows the products that are formed when butane $\left( C _4 H _{10}\right)$ is combusted.
$2 C_4 H_{10}+13 O_2 \rightarrow 8 CO_2+10 H_2 O$
What is the mole ratio of butane to carbon dioxide?
A. 2:8
B. 1:5
C. 13:8
D. 13:10
Answer (2)
The mole ratio of butane to carbon dioxide in the combustion reaction is 2:8. This means that for every 2 moles of butane, 8 moles of carbon dioxide are produced. Therefore, the correct answer option is 2:8.
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Identify the mole coefficients of butane and carbon dioxide from the balanced equation.
Express the mole ratio of butane to carbon dioxide as a fraction: 8 2 .
Simplify the fraction to its simplest form: 4 1 .
The mole ratio of butane to carbon dioxide is 2 : 8 .
Explanation
Analyze the Balanced Equation The balanced chemical equation provided is:
2 C 4 H 10 + 13 O 2 → 8 C O 2 + 10 H 2 O
We need to find the mole ratio of butane ( C 4 H 10 ) to carbon dioxide ( C O 2 ).
Identify Moles of Butane and Carbon Dioxide From the balanced equation, we can see that 2 moles of butane ( C 4 H 10 ) react to produce 8 moles of carbon dioxide ( C O 2 ).
Express the Mole Ratio The mole ratio of butane to carbon dioxide is therefore:
moles of carbon dioxide moles of butane = 8 2
Simplify the Ratio We simplify the fraction to its simplest form:
8 2 = 4 1
So, the mole ratio of butane to carbon dioxide is 1:4.
Re-examine and Choose the Correct Option However, the options provided do not include 1:4. Let's re-examine the given options and the balanced equation to ensure we haven't made an error. The balanced equation clearly shows a 2:8 relationship between butane and carbon dioxide, which simplifies to 1:4. Among the given options, 2:8 is listed, which is equivalent to 1:4 before simplification.
Final Answer Confirmed Therefore, the correct mole ratio of butane to carbon dioxide is 2:8, which simplifies to 1:4.
Examples
In cooking, mole ratios are essential for scaling recipes. If a recipe calls for a certain amount of one ingredient relative to another, understanding mole ratios helps you adjust the quantities accurately. For example, if you're baking a cake and the recipe specifies a ratio of flour to sugar, knowing this ratio ensures the cake has the right texture and sweetness. Similarly, in chemistry, mole ratios are used to determine the amount of reactants needed to produce a specific amount of product, ensuring reactions proceed efficiently and completely.
