Select the correct answer.
Excess sodium hydroxide is added to a solution containing 4.6 grams of magnesium chloride. A reaction takes place according to this equation:
[tex]2 NaOH(aq)+MgCl_2(aq) \rightarrow 2 NaCl(aq)+Mg(OH)_2(s)[/tex]
The magnesium hydroxide produced by the reaction was collected and weighed. If the mass of the magnesium hydroxide was 2.7 grams, what was the percent yield? Use the periodic table.
A. [tex]48 \%[/tex]
B. [tex]59 \%[/tex]
C. [tex]61 \%[/tex]
D. [tex]96 \%[/tex]
Answer (2)
Calculate the molar mass of M g C l 2 : 24.305 + 2 × 35.453 = 95.211 g/mol .
Calculate moles of M g C l 2 : 95.211 4.6 = 0.0483 mol .
Calculate the molar mass of M g ( O H ) 2 : 24.305 + 2 × ( 15.999 + 1.008 ) = 58.319 g/mol .
Calculate the percent yield: 0.0483 × 58.319 2.7 × 100 = 95.83% ≈ 96% . The final answer is 96% .
Explanation
Calculate Molar Mass of Magnesium Chloride First, we need to calculate the molar mass of magnesium chloride ( M g C l 2 ). The molar mass of Mg is 24.305 g/mol and the molar mass of Cl is 35.453 g/mol. Therefore, the molar mass of M g C l 2 is: 24.305 + 2 × 35.453 = 95.211 g/mol
Calculate Moles of Magnesium Chloride Next, we calculate the number of moles of M g C l 2 used in the reaction: Moles of M g C l 2 = Molar mass of M g C l 2 Mass of M g C l 2 = 95.211 g/mol 4.6 g = 0.0483 mol
Calculate Molar Mass of Magnesium Hydroxide Now, we calculate the molar mass of magnesium hydroxide ( M g ( O H ) 2 ). The molar mass of Mg is 24.305 g/mol, O is 15.999 g/mol, and H is 1.008 g/mol. Therefore, the molar mass of M g ( O H ) 2 is: 24.305 + 2 × ( 15.999 + 1.008 ) = 58.319 g/mol
Determine Theoretical Moles of Magnesium Hydroxide From the balanced equation, 2 N a O H ( a q ) + M g C l 2 ( a q ) → 2 N a Cl ( a q ) + M g ( O H ) 2 ( s ) , we see that 1 mole of M g C l 2 produces 1 mole of M g ( O H ) 2 . Therefore, the theoretical number of moles of M g ( O H ) 2 produced is equal to the number of moles of M g C l 2 used, which is 0.0483 mol.
Calculate Theoretical Mass of Magnesium Hydroxide Now, we calculate the theoretical mass of M g ( O H ) 2 that can be produced: Theoretical mass of M g ( O H ) 2 = Moles of M g ( O H ) 2 × Molar mass of M g ( O H ) 2 Theoretical mass of M g ( O H ) 2 = 0.0483 mol × 58.319 g/mol = 2.817 g
Calculate Percent Yield The actual yield of M g ( O H ) 2 is given as 2.7 grams. Now we can calculate the percent yield: Percent Yield = Theoretical Yield Actual Yield × 100 Percent Yield = 2.817 g 2.7 g × 100 = 95.83%
Final Answer Therefore, the percent yield of the reaction is approximately 96%.
Examples
Percent yield is a concept used extensively in chemical manufacturing and pharmaceutical industries. For example, when synthesizing a new drug, chemists need to optimize the reaction conditions to maximize the yield of the desired product. A higher percent yield not only reduces waste but also lowers production costs, making the process more efficient and economically viable. Understanding and calculating percent yield helps in assessing the success and efficiency of chemical reactions in various practical applications.
The percent yield of magnesium hydroxide produced in the reaction is approximately 96%. This value indicates the efficiency of the chemical reaction based on the actual and theoretical yields. The correct answer is D: 96%.
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