the dencity of 3 molal solution of NaOH is 1.110g/mL calculate the molarity of the solution

Density = Mass/Volume

Volume = 40/1.110
V = 36.03 ml
M = 120/40 * 1000/36.03
M = 83.26 M

Note the correct spelling of density. Probably a typo.

3 m = 3 mols/kg solvent.
molar mass NaOH = 40 grams; therefore, 3 mols = 120 grams.
The solution is 1000 g solvent + 120 g NaOH = total of 1000+120 = 1120g.
Use density to convert to volume in mL and convert to L, then M = mols/L soln.

To calculate the molarity of a solution, we need to know the density and molar mass of the solute, as well as the mass of the solute dissolved in a known volume of the solution.

Given:
Density of a 3 molal solution of NaOH = 1.110 g/mL

First, let's convert the density to grams per cubic centimeter (g/cm³) because it is the preferred unit for density calculations:

Density = 1.110 g/mL = 1.110 g/cm³

Now, we need to calculate the mass of NaOH dissolved in a known volume of the solution. Since it is a 3 molal solution, it means that there are 3 moles of NaOH present in 1 kg (1000 g) of the solvent (water).

To find the mass of NaOH in the solution, we can use the molecular weight of NaOH, which is approximately 40 g/mol.

Mass of NaOH = 3 mol x 40 g/mol = 120 g

Now, we have the mass of NaOH (120 g) dissolved in a known volume of the solution (1000 g or 1 L since the density is given in g/mL).

Molarity (M) is defined as the number of moles of solute per liter (L) of solution.

Molarity (M) = Moles of solute (NaOH) / Volume of solution (L)

Since we already have the mass of solute and the density of the solution, we can calculate the volume of the solution as follows:

Volume of solution = Mass of solution / Density of solution

Volume of solution = 1000 g / 1.110 g/cm³ = 900.90 cm³ ≈ 0.9009 L

Now we can calculate the molarity:

Molarity (M) = Moles of solute (NaOH) / Volume of solution (L)

Molarity (M) = 120 g / 0.9009 L ≈ 133.26 M

Therefore, the molarity of the 3 molal solution of NaOH is approximately 133.26 M.

To calculate the molarity (M) of a solution, we need to know the number of moles of solute (NaOH) dissolved in a given volume of solution (in liters).

In this case, we are given the density of the solution, which is 1.110 g/mL. To find the content of NaOH in the 3 molal solution, we first need to convert the density to grams per liter (g/L) since the molarity is calculated based on liters.

To convert the density from grams per milliliter (g/mL) to grams per liter (g/L), we multiply by 1000, since there are 1000 mL in one liter:

Density (g/L) = 1.110 g/mL * 1000 mL/L = 1110 g/L

Now we have the density in grams per liter.

Next, we need to calculate the grams of NaOH in the solution. For a molal (mol/kg) solution, there are 3 mol of solute (NaOH) dissolved in 1 kg of solvent (water). This means that for every 3 moles of NaOH, there is 1 kg of water.

Since we know the molar mass of NaOH is 22.99 g/mol + 16.00 g/mol + 1.01 g/mol = 40.00 g/mol, we can calculate the grams of NaOH in the solution as follows:

Grams of NaOH = 3 mol * 40.00 g/mol = 120 g

Now we know that there are 120 grams of NaOH in 1 kg (1000 g) of water.

But we need to find the molarity, so we need to find the moles of NaOH in the solution. To calculate this, we divide the grams of NaOH by the molar mass:

Moles of NaOH = 120 g / 40.00 g/mol = 3 mol

Since we know the number of moles and the volume in liters, we can calculate the molarity:

Molarity (M) = Moles of NaOH / Volume of solution (L)

However, we still need to know the volume of the solution. Without that information, we cannot calculate the molarity.