A scientist wants to determine how many moles of gold (III) sulfite [tex]$\left( Au _2\left( SO _3\right)_3\right)$[/tex] would be needed to react completely with 6.65 mol of sodium nitrate ([tex]$NaNO _3$[/tex]).
[tex]$6 NaNO_3+Au_2\left(SO_3\right)_3 \rightarrow 3 Na_2 SO_3+2 Au\left(NO_3\right)_3$[/tex]
How many moles of gold (III) sulfite would be needed?
[tex]$6.65 mol NaNO _3$[/tex]
Answer (1)
Use the balanced chemical equation to identify the mole ratio between N a N O 3 and A u 2 ( S O 3 ) 3 , which is 6:1.
Set up a proportion to relate the moles of N a N O 3 given (6.65 mol) to the moles of A u 2 ( S O 3 ) 3 needed.
Solve the proportion to find the moles of A u 2 ( S O 3 ) 3 required: 6 1 × 6.65 = 1.108333...
Round the result to two decimal places to get the final answer: 1.11
Explanation
Analyze the problem We are given the balanced chemical equation: 6 N a N O 3 + A u 2 ( S O 3 ) 3 → 3 N a 2 S O 3 + 2 A u ( N O 3 ) 3 This equation tells us that 6 moles of sodium nitrate ( N a N O 3 ) react completely with 1 mole of gold (III) sulfite ( A u 2 ( S O 3 ) 3 ). We are given that we have 6.65 moles of N a N O 3 and we want to find out how many moles of A u 2 ( S O 3 ) 3 are needed to react with all of the N a N O 3 .
Determine the mole ratio To find the required moles of A u 2 ( S O 3 ) 3 , we use the mole ratio from the balanced equation. The ratio of A u 2 ( S O 3 ) 3 to N a N O 3 is 1:6. This means that for every 6 moles of N a N O 3 , we need 1 mole of A u 2 ( S O 3 ) 3 .
Set up the proportion Now, we can set up a proportion to find the moles of A u 2 ( S O 3 ) 3 needed: m o l es o f N a N O 3 m o l es o f A u 2 ( S O 3 ) 3 = 6 1 We are given 6.65 moles of N a N O 3 , so we can plug that into the equation: 6.65 m o l es o f A u 2 ( S O 3 ) 3 = 6 1
Solve for moles of gold (III) sulfite To solve for the moles of A u 2 ( S O 3 ) 3 , we multiply both sides of the equation by 6.65: m o l es o f A u 2 ( S O 3 ) 3 = 6 1 × 6.65 m o l es o f A u 2 ( S O 3 ) 3 = 1.108333...
Final Answer Therefore, 1.108333... moles of A u 2 ( S O 3 ) 3 are needed to react completely with 6.65 moles of N a N O 3 . Rounding to two decimal places, we get 1.11 moles.
Examples
In chemistry, stoichiometry is essential for calculating the amounts of reactants and products in chemical reactions. For instance, if you're synthesizing a new drug, you need to know the exact amount of each ingredient to ensure the reaction proceeds correctly and efficiently. This problem demonstrates how to use mole ratios from a balanced equation to determine the quantity of one reactant needed to fully react with another, which is crucial in pharmaceutical research and chemical manufacturing to optimize processes and minimize waste.
