The density of concentrated sulfuric acid is 1.84 g/mL. If this corresponds to 18 M, what is the molality of the solution?

Molar mass= 98.
98 x 18 =1764g/L - 1.84 =1762.16/1000 = 1.76 kg
18/1.76=10.23 m

But my only options are:
a) 18 m
b) 95.5 m
c) 240 m
d) 0.240 m?

18 mols x 98 g/mol = 1764 grams/L of H2SO4.

mass solution is 1.84 x 1000 = 1840 grams.
mass H2O then is 1840-1764 = 76 grams.
m = mol/kg solvent = 18/0.076 = ?

To find the molality of the solution, we need to convert the density (in g/mL) to the molar concentration (in mol/L) and then to molality (in mol/kg).

First, calculate the molar concentration (in mol/L):

Molar concentration (M) = 18 M

Next, convert the molar concentration to grams per liter (g/L):

Molar mass of sulfuric acid (H2SO4) = 98 g/mol
18 M x 98 g/mol = 1764 g/L

Now, convert the density from g/mL to kg/L:

Density = 1.84 g/mL
1.84 g/mL x 1000 mL/L = 1840 g/L
1840 g/L ÷ 1000 = 1.84 kg/L

Finally, calculate the molality (m) using the equation:

molality (m) = Molar concentration (mol/L) ÷ density (kg/L)

molality (m) = 18 mol/L ÷ 1.84 kg/L
molality (m) ≈ 9.78 m

None of the given answer options (a, b, c, d) matches the calculated molality of approximately 9.78 m.

To find the molality of the solution, we need to know the amount of solute (in moles) present in a given mass of the solvent (in kilograms). In this case, the given information is the density of concentrated sulfuric acid (1.84 g/mL) and its corresponding molarity (18 M).

First, let's determine the molar mass of sulfuric acid, which is 98 g/mol. This information is given in the question.

Next, we need to convert the density from grams per milliliter to kilograms per liter. To do this, we divide the density by 1000.

1.84 g/mL = 1.84 g/mL ÷ 1000 = 0.00184 kg/mL

Then, we subtract the density of the solution (1.84 g/mL or 0.00184 kg/mL) from the molar mass (1764 g/L or 1.764 kg/L):

1.764 kg/L - 0.00184 kg/mL = 1.76216 kg/L

Now, we have the mass of sulfuric acid in 1 liter of the solution.

But we want to find the molality, which is defined as moles of solute per kilogram of solvent. To calculate the kilogram of the solvent, we divide the mass of the solution (1.76216 kg) by its density (1.84 g/mL or 0.00184 kg/mL):

1.76216 kg ÷ 0.00184 kg/mL = 956.17 mL

Therefore, the solution contains approximately 956.17 mL (or 0.95617 L) of sulfuric acid.

Finally, we can calculate the molality by dividing the molarity (18 M) by the mass of the solvent in kilograms (0.95617 kg):

18 M ÷ 0.95617 kg = 18.80 m

Comparing the calculated molality (18.80 m) with the options given, it seems that none of the options provided match the calculated result.