During a water treatment program, 127 grams of calcium nitrate, [tex]Ca (NO _3)_2[/tex], is dissolved in water. The final volume of the solution is 2,300 milliliters. What is the molarity of the solution?
Refer to the periodic table to help you answer. Express your answer to two significant figures.
The molarity of the solution is $\square$ M.
Answer (2)
Calculate the molar mass of C a ( N O 3 ) 2 : 164.1 \t g / m o l .
Convert the volume of the solution to liters: 2.3 \t L .
Calculate the number of moles of C a ( N O 3 ) 2 : 0.7739 \t m o l .
Calculate the molarity: \t M o l a r i t y = 2.3 \t L 0.7739 \t m o l = 0.34 \t M .
The molarity of the solution is 0.34 M.
Explanation
Problem Analysis We are given that 127 grams of calcium nitrate, C a ( N O 3 ) 2 , is dissolved in 2,300 milliliters of water. We need to find the molarity of the solution, expressed to two significant figures. Molarity is defined as the number of moles of solute per liter of solution.
Calculating Molar Mass First, we need to calculate the molar mass of calcium nitrate, C a ( N O 3 ) 2 . The atomic masses are: Ca = 40.08 g/mol, N = 14.01 g/mol, O = 16.00 g/mol. Therefore, the molar mass of C a ( N O 3 ) 2 is calculated as follows: 40.08 + 2 ( 14.01 + 3 ( 16.00 )) = 40.08 + 2 ( 14.01 + 48.00 ) = 40.08 + 2 ( 62.01 ) = 40.08 + 124.02 = 164.10 \t g / m o l So, the molar mass of C a ( N O 3 ) 2 is 164.1 g/mol.
Converting Volume Next, we convert the volume of the solution from milliliters to liters: 2300 \t m L = 1000 2300 = 2.3 \t L
Calculating Moles Now, we calculate the number of moles of calcium nitrate: \t m o l es = \t m o l a r ma ss \t ma ss = 164.1 \t g / m o l 127 \t g = 0.7739 \t m o l
Calculating Molarity Finally, we calculate the molarity of the solution: \t M o l a r i t y = \t l i t erso f so l u t i o n \t m o l eso f so l u t e = 2.3 \t L 0.7739 \t m o l = 0.3365 \t M Rounding the answer to two significant figures, we get 0.34 M.
Final Answer Therefore, the molarity of the solution is 0.34 M.
Examples
Molarity is a crucial concept in chemistry, especially in fields like medicine and environmental science. For instance, when preparing medications, pharmacists need to calculate the exact molarity of solutions to ensure the correct dosage. Similarly, in environmental monitoring, knowing the molarity of pollutants in water helps scientists assess the level of contamination and devise appropriate treatment strategies. Understanding molarity ensures accuracy and effectiveness in various applications, from healthcare to environmental protection.
The molarity of the calcium nitrate solution, after calculating its molar mass, converting volume to liters, and determining the number of moles, is found to be 0.34 M. This was done by dividing the moles of solute by the solution's volume in liters. The final answer is expressed to two significant figures.
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