Middle School

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------------------------------------------------ How many grams of solute are needed to make a 1.00 m solution of HNO₃ in 2.00 kg of water?

A. 126 g HNO₃
B. 31.5 g HNO₃
C. 63.0 g HNO₃
D. 98.1 g HNO₃

Answer :

Final answer:

To make a 1.00m solution of HNO₃ in 2.00 kg of water, (a) 126g of HNO₃ are required. This is calculated using the molar mass of HNO₃ and the definition of molality, which involves moles of solute per kilogram of solvent. Hence, (a) is the correct option.

Explanation:

To find out how many grams of solute (HNO₃) are needed to make a 1.00m solution of HNO₃ in 2.00 kg of water, we need to calculate the molality (m) of the solution. Molality is the solute to solvent ratio expressed in moles per kilogram.

First, we determine the molar mass of HNO₃.

Using the molar masses of hydrogen (H), nitrogen (N), and oxygen (O), the molar mass is calculated as: 1(1.01 g/mol) + 1(14.01 g/mol) + 3(16.00 g/mol) = 63.01 g/mol for HNO₃. With this information, we can calculate the mass of the solute required for a 1.00 m solution.

Molality (m) = moles of solute / kg of solvent
1.00 m = moles of HNO₃ / 2.00 kg
moles of HNO₃ = 1.00 m * 2.00 kg = 2.00 moles.

To find the mass of solute in grams, we multiply the number of moles by the molar mass:
Mass of HNO₃ = moles of HNO₃ * molar mass of HNO₃
Mass of HNO₃ = 2.00 moles * 63.01 g/mol = 126.02 g.

Thus, 126g of HNO₃ are needed to create a 1.00m solution in 2.00 kg of water.