A solution of H2SO4(aq) with a molal concentration of 1.66 m has a density of 1.104 g/mL. What is the molar concentration of this solution?

To find the molar concentration of the solution, also known as the molarity (M), we can use the formula:

Molarity (M) = molality (m) * density (ρ) / molar mass (MM)

Given data:
Molality (m) = 1.66 m
Density (ρ) = 1.104 g/mL

Now, we need to calculate the molar mass (MM) of H2SO4.

The molar mass of hydrogen (H) is approximately 1.01 g/mol.
The molar mass of sulfur (S) is approximately 32.07 g/mol.
The molar mass of oxygen (O) is approximately 16.00 g/mol.

To calculate the molar mass of H2SO4, we multiply the molar mass of each element by its respective subscript and sum them up:

Molar mass (MM) = (2 * molar mass of H) + molar mass of S + (4 * molar mass of O)

Molar mass (MM) = (2 * 1.01 g/mol) + 32.07 g/mol + (4 * 16.00 g/mol)
Molar mass (MM) = 2.02 g/mol + 32.07 g/mol + 64.00 g/mol
Molar mass (MM) = 98.09 g/mol

Now we can substitute the values in the formula:

M = m * ρ / MM
M = 1.66 m * 1.104 g/mL / 98.09 g/mol

First, we need to convert the density from g/mL to g/L by multiplying it by 1000:

M = 1.66 m * (1.104 g/mL * 1000 mL/L) / 98.09 g/mol
M = 1.66 m * 1104 g/L / 98.09 g/mol

Now we can simplify the equation:

M = 18.35 mol ⋅ kg ^−1 * 1104 kg ⋅ L ^−1 / 98.09 g ⋅ mol ^−1
M = 20250.4 g ⋅ L ^−1 / (98.09 g ⋅ mol ^−1 * 1000 g/ mol)
M ≈ 0.2063 mol ⋅ L ^−1

Therefore, the molar concentration of the solution is approximately 0.2063 M.

To find the molar concentration of the solution, we need to convert the given molal concentration to a molar concentration using the density of the solution.

Step 1: Find the molar mass of H2SO4
The molar mass of H2SO4 can be calculated by adding up the atomic masses of all the atoms in the compound.
H2SO4 = (2 * 1.01 g/mol) + (32.07 g/mol) + (4 * 16.00 g/mol) = 98.09 g/mol

Step 2: Calculate the moles of H2SO4 in the given solution
Since the molal concentration is given in moles of solute per kilogram of solvent, we can calculate the moles of H2SO4 in the solution using the given density.
Density = mass/volume
volume = mass/density

The volume of 1 kg of the solution can be calculated as follows:
volume = (1 kg)/(1.104 g/mL)

Now we can calculate the mass of H2SO4 in 1 kg of the solution:
mass of H2SO4 = molal concentration * molar mass * mass of solvent
mass = 1.66 mol/kg * 98.09 g/mol * (1 kg)/(1.104 g/mL)

Step 3: Convert the mass of H2SO4 to moles
moles = mass/molar mass

Step 4: Calculate the molar concentration
Molar concentration = moles/volume

Now, let's calculate the molar concentration:

mass of H2SO4 = 1.66 mol/kg * 98.09 g/mol * (1 kg)/(1.104 g/mL) = 139.32 mol/L

moles = 139.32 g / 98.09 g/mol = 1.42 mol

volume = (1 kg)/(1.104 g/mL) = 904 mL = 0.904 L

Molar concentration = 1.42 mol / 0.904 L = 1.57 M

Therefore, the molar concentration of the solution is 1.57 M.

1.66m means 1.66 mol/kg solvent.

1.66 mol x 98 g/mol = about 163 g H2SOO$ BUT THIS IS JUST AN ESTIMATE.
Total solution then is 1000 g + 163 = ABOUT 1163g. Convert that to L, then
M = mols/L.