Calculate the mass of ammonium sulfide $(NH_4)_2S$ in 3.00 L of a 0.0200 M solution.
Answer (2)
Calculate the molar mass of ( N H 4 ) 2 S as 68.154 g/mol.
Determine the number of moles of ( N H 4 ) 2 S using the formula: M o l es = M o l a r i t y × V o l u m e = 0.0200 M × 3.00 L = 0.06 m o l .
Calculate the mass of ( N H 4 ) 2 S using the formula: M a ss = M o l es × M o l a r M a ss = 0.06 m o l × 68.154 g / m o l = 4.08924 g .
The mass of ammonium sulfide in the solution is approximately 4.09 g.
Explanation
Problem Analysis We are asked to calculate the mass of ammonium sulfide, ( N H 4 ) 2 S , in a 3.00 L solution with a concentration of 0.0200 M. To do this, we will first calculate the number of moles of ammonium sulfide present in the solution, and then use the molar mass of ammonium sulfide to convert moles to grams.
Calculating Molar Mass First, we need to calculate the molar mass of ammonium sulfide, ( N H 4 ) 2 S . The molar mass is the sum of the atomic masses of each element in the compound, multiplied by the number of times that element appears in the compound.
The molar mass of nitrogen (N) is 14.01 g/mol. The molar mass of hydrogen (H) is 1.008 g/mol. The molar mass of sulfur (S) is 32.07 g/mol.
So, the molar mass of ( N H 4 ) 2 S is calculated as follows:
M o l a r ma ss o f ( N H 4 ) 2 S = 2 × ( 14.01 + 4 × 1.008 ) + 32.07 M o l a r ma ss o f ( N H 4 ) 2 S = 2 × ( 14.01 + 4.032 ) + 32.07 M o l a r ma ss o f ( N H 4 ) 2 S = 2 × 18.042 + 32.07 M o l a r ma ss o f ( N H 4 ) 2 S = 36.084 + 32.07 M o l a r ma ss o f ( N H 4 ) 2 S = 68.154 g / m o l
Calculating Moles Next, we calculate the number of moles of ( N H 4 ) 2 S in the solution using the formula:
M o l es = M o l a r i t y × V o l u m e
Given that the molarity is 0.0200 M and the volume is 3.00 L:
M o l es = 0.0200 M × 3.00 L M o l es = 0.06 m o l
Calculating Mass Now, we can calculate the mass of ( N H 4 ) 2 S using the formula:
M a ss = M o l es × M o l a r M a ss
M a ss = 0.06 m o l × 68.154 g / m o l M a ss = 4.08924 g
Therefore, the mass of ammonium sulfide in the solution is approximately 4.09 g.
Final Answer The mass of ammonium sulfide ( N H 4 ) 2 S in 3.00 L of a 0.0200 M solution is approximately 4.09 g.
Examples
Understanding molarity and how to calculate the mass of a compound in a solution is crucial in many real-world applications. For instance, in agriculture, farmers need to prepare fertilizer solutions with specific concentrations to ensure their crops receive the right amount of nutrients. Similarly, in medicine, pharmacists must accurately calculate the mass of active ingredients needed to compound medications. In environmental science, chemists determine the concentration of pollutants in water samples to assess water quality. Knowing how to convert between volume, molarity, and mass allows professionals to prepare solutions accurately, ensuring desired outcomes in various fields.
To calculate the mass of ammonium sulfide ( N H 4 ) 2 S in a 3.00 L solution with a concentration of 0.0200 M, we first determined its molar mass to be 68.154 g/mol. Then, we calculated the number of moles in the solution, which is 0.06 mol. Finally, we used the moles and molar mass to find that the mass is approximately 4.09 g.
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