Questions: A balanced chemical equation indicates the proportions or ratios of the various reactants and products to one another. From the coefficients in the balanced chemical equation, we can create mole-mole ratios that relate any of the various chemicals to a different chemical. For example, consider the following balanced chemical equation: N2(g)+3 H2(g) rightarrow 2 NH3(g) From this equation, there are several possible mole-mole ratios. Two of these mole-mole ratios are the following: 3 moles H2/1 mole N2 or 2 moles NH3/3 moles H2 How many moles of sodium nitride, NaN3, are needed to produce 3.94 moles of nitrogen, N2? 2 NaN3(s) rightarrow 2 Na(s)+3 N2(g) 5.91 moles of NaN3 3.94 moles of NaN3 3.80 moles of NaN3 2.63 moles of NaN3

A balanced chemical equation indicates the proportions or ratios of the various reactants and products to one another. From the coefficients in the balanced chemical equation, we can create mole-mole ratios that relate any of the various chemicals to a different chemical. For example, consider the following balanced chemical equation: N2(g)+3 H2(g) rightarrow 2 NH3(g) From this equation, there are several possible mole-mole ratios. Two of these mole-mole ratios are the following: 3 moles H2/1 mole N2 or 2 moles NH3/3 moles H2 How many moles of sodium nitride, NaN3, are needed to produce 3.94 moles of nitrogen, N2? 2 NaN3(s) rightarrow 2 Na(s)+3 N2(g) 5.91 moles of NaN3 3.94 moles of NaN3 3.80 moles of NaN3 2.63 moles of NaN3
Transcript text: A balanced chemical equation indicates the proportions or ratios of the various reactants and products to one another. From the coefficients in the balanced chemical equation, we can create mole-mole ratios that relate any of the various chemicals to a different chemical. For example, consider the following balanced chemical equation: \[ \mathrm{N}_{2}(\mathrm{~g})+3 \mathrm{H}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{NH}_{3}(\mathrm{~g}) \] From this equation, there are several possible mole-mole ratios. Two of these mole-mole ratios are the following: \[ \frac{3 \text { moles } \mathrm{H}_{2}}{1 \text { mole } \mathrm{N}_{2}} \text { or } \frac{2 \text { moles } \mathrm{NH}_{3}}{3 \text { moles } \mathrm{H}_{2}} \] How many moles of sodium nitride, $\mathrm{NaN}_{3}$, are needed to produce 3.94 moles of nitrogen, $\mathrm{N}_{2}$ ? \[ 2 \mathrm{NaN}_{3}(\mathrm{~s}) \rightarrow 2 \mathrm{Na}(\mathrm{~s})+3 \mathrm{~N}_{2}(g) \] 5.91 moles of $\mathrm{NaN}_{3}$ 3.94 moles of $\mathrm{NaN}_{3}$ 3.80 moles of $\mathrm{NaN}_{3}$ 2.63 moles of $\mathrm{NaN}_{3}$ submit IDON'T KNOWYET
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Solution

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Solution Steps

Step 1: Identify the Mole-Mole Ratio

From the balanced chemical equation: \[ 2 \mathrm{NaN}_{3}(\mathrm{~s}) \rightarrow 2 \mathrm{Na}(\mathrm{~s}) + 3 \mathrm{~N}_{2}(g) \] we can identify the mole-mole ratio between sodium nitride (\(\mathrm{NaN}_{3}\)) and nitrogen (\(\mathrm{N}_{2}\)). The ratio is: \[ \frac{2 \text{ moles } \mathrm{NaN}_{3}}{3 \text{ moles } \mathrm{N}_{2}} \]

Step 2: Set Up the Proportion

We need to find how many moles of \(\mathrm{NaN}_{3}\) are required to produce 3.94 moles of \(\mathrm{N}_{2}\). Using the mole-mole ratio: \[ \frac{2 \text{ moles } \mathrm{NaN}_{3}}{3 \text{ moles } \mathrm{N}_{2}} = \frac{x \text{ moles } \mathrm{NaN}_{3}}{3.94 \text{ moles } \mathrm{N}_{2}} \]

Step 3: Solve for \(x\)

Cross-multiply to solve for \(x\): \[ 2 \times 3.94 = 3 \times x \] \[ 7.88 = 3x \] \[ x = \frac{7.88}{3} = 2.6267 \]

Step 4: Round to Four Significant Digits

Round the result to four significant digits: \[ x = 2.627 \]

Final Answer

\[ \boxed{2.63 \text{ moles of } \mathrm{NaN}_{3}} \]

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