A 20.0% (w/w) aqueous solution of NaOH has a density of 1.125 g/cm^3. What is the molarity (M) of this solution?
In one neat and tidy equation it is
1.125 g/cc x 1000 cc x (20/100) x (1 mol/40g) = ? Molar
In pieces.
mass of 1000 cc is 1.125 g/cc x 1000 cc = ?
mass of NaOH in that 1000 cc solution is ?mass x 0.20 = ?
mols NaOH in that mass NaOH is ?grams/molar mass
All of that gives you mols NaOH/L solution and that's the definition of molarity.
To find the molarity (M) of the solution, we need to convert the given weight/volume percentage (w/w) to a molar concentration.
Step 1: Calculate the weight of NaOH in the solution.
Assuming we have 100 g of the solution, the weight of NaOH present is 20.0% of 100 g = 20.0 g.
Step 2: Calculate the moles of NaOH using its molar mass.
The molar mass of NaOH is the atomic mass of Na plus the atomic mass of O plus the atomic mass of H:
Na: 22.99 g/mol
O: 16.00 g/mol
H: 1.01 g/mol
Molar mass of NaOH = 22.99 + 16.00 + 1.01 = 40.00 g/mol
The moles of NaOH can be calculated using the formula:
moles = mass / molar mass
moles = 20.0 g / 40.00 g/mol = 0.50 mol
Step 3: Calculate the volume of the solution using the density.
Density = mass / volume
Rearranging the equation, we get:
Volume = mass / density
Volume = 100 g / 1.125 g/cm^3 = 88.88 cm^3
Step 4: Convert volume from cm^3 to liters.
Volume (in L) = 88.88 cm^3 * (1 L / 1000 cm^3) = 0.08888 L
Step 5: Calculate the molarity (M) of the solution.
Molarity (M) = moles / volume
Molarity (M) = 0.50 mol / 0.08888 L = 5.62 M
Therefore, the molarity (M) of the 20.0% (w/w) aqueous solution of NaOH is 5.62 M.
To determine the molarity (M) of the NaOH solution, we need to understand the relationship between molarity, percentage concentration, and density.
Molarity is defined as the number of moles of solute per liter of solution. In this case, the solute is NaOH and the solution has a known density of 1.125 g/cm^3.
Given that the solution is a 20.0% (w/w) aqueous solution of NaOH, it means that 20.0 grams of NaOH is present in every 100 grams of the solution.
To determine the molarity, we need to convert the given information into moles of NaOH.
Step 1: Convert the density from grams per cubic centimeter (g/cm^3) to grams per milliliter (g/mL) since molarity is expressed in liters:
Density = 1.125 g/cm^3 = 1.125 g/mL
Step 2: Calculate the volume of the solution:
Mass = 100 grams (since it is a 100 gram solution from the percentage given)
Density = Mass/Volume
Volume = Mass/Density = 100 g / 1.125 g/mL = 88.89 mL
Step 3: Calculate the moles of NaOH:
Since the solution is 20.0% (w/w) NaOH, we have 20 grams of NaOH in 100 grams of the solution.
Molar mass of NaOH = 22.99 g/mol (Na) + 16.00 g/mol (O) + 1.01 g/mol (H) = 39.99 g/mol
Moles of NaOH = Mass of NaOH / Molar mass of NaOH = 20 g / 39.99 g/mol = 0.500 mol
Step 4: Calculate the molarity:
Molarity (M) = Moles of NaOH / Volume of solution (in liters) = 0.500 mol / 0.08889 L = 5.63 M
Therefore, the molarity (M) of the 20.0% (w/w) NaOH aqueous solution is 5.63 M.