How many moles of H2SO4 are present in 250 g of an aqueous solution that is 4.8 m (molal)? The density of the solution is1.58 g/mL.
m = mols/kg solution.
So a 4.8 m soln is 4.8 mol/kg soln.
If you have 4.8 mols in 1 kg how much do you have in 250 g? Wouldn't that just be 4.8 mols x (250 g/1000 g) = ? = say 4.8/4 = 1.2 mols
To calculate the number of moles of H2SO4 in the given solution, you need to follow these steps:
Step 1: Determine the mass of the solution.
Given the density of the solution (1.58 g/mL) and the volume of the solution, you can find the mass of the solution. The volume is not provided in the question, so you'll need to skip this step for now and come back to it later.
Step 2: Calculate the mass of H2SO4.
The molality (m) is defined as the number of moles of solute per kilogram of solvent. In this case, the solute is H2SO4, and the solvent is water. Assuming the density of the solution is the same as that of water (1 g/mL), you can convert the mass of the solution (250 g) to the mass of water, which is the solvent. To do this, divide the mass of the solution by the density of water (1 g/mL), giving you the mass of water in the solution.
Step 3: Calculate the number of moles.
Now that you know the mass of H2SO4 and the mass of water, you can calculate the number of moles of H2SO4 using the molality. The molality is given as 4.8 m, which means there are 4.8 moles of H2SO4 in 1 kg of water. So, to calculate the number of moles of H2SO4 in the given solution, multiply the mass of H2SO4 (from step 2) by the molality (4.8 m).
Step 4: Convert the moles to grams.
If you need to express the answer in grams, multiply the number of moles of H2SO4 by the molar mass of H2SO4, which is 98.09 g/mol.
Now, let's go through these steps in detail:
Step 1: Determine the mass of the solution.
The mass of the solution is given as 250 g. Since the volume of the solution is not provided, we cannot directly calculate the mass of water in the solution. We will need to come back to this step later.
Step 2: Calculate the mass of H2SO4.
The molality (m) is given as 4.8 m. Molality is defined as the number of moles of solute per kilogram of solvent. In this case, the solute is H2SO4, and the solvent is water. Given that the molality is expressed in moles of H2SO4 per kilogram of water, you need to convert the mass of the solution (250 g) to the mass of water. Since the density of the solution is 1.58 g/mL, you can assume the density of water is also 1 g/mL. Thus, the mass of water in the solution is 250 g.
Step 3: Calculate the number of moles.
To find the moles of H2SO4, you need to multiply the mass of H2SO4 by the molality. Since the molality is given as 4.8 m and the mass of H2SO4 is the same as the mass of water (250 g), the number of moles of H2SO4 is:
Number of moles = mass of H2SO4 (in kg) x molality
= (250 g / 1000 g/kg) x 4.8 mol/kg
= 1.2 mol
Therefore, there are 1.2 moles of H2SO4 in the given solution.
Step 4: Convert moles to grams.
If you want to express the answer in grams, multiply the number of moles of H2SO4 by the molar mass of H2SO4:
Number of grams = number of moles x molar mass
= 1.2 mol x 98.09 g/mol
= 117.708 g
Therefore, there are 117.708 grams of H2SO4 in the given solution.
Note: In step 1, since the density of the solution was provided, you can use it to calculate the volume of the solution. Then, using the density of water (1 g/mL), you can convert the volume to mass of water. However, in this question, the density of water is not provided, so we cannot directly calculate the mass of water.