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.
