A bottle of concentrated sulphuric acid (Density =1.80 gcm/cm cube) is labelled as 86% by weight. What is the molarity of the solution?
A bottle of concentrated
To find the molarity of a solution, we need to know the molecular weight of the solute and the volume of the solution.
In this case, the solute is sulphuric acid (H2SO4), and the concentration is given in weight percent (86% by weight).
Step 1: Calculate the molecular weight of sulphuric acid (H2SO4).
Atomic masses:
H = 1.01 g/mol
S = 32.07 g/mol
O = 16.00 g/mol
Molecular weight of H2SO4:
2(H) + 1(S) + 4(O) = (2 x 1.01 g/mol) + 32.07 g/mol + (4 x 16.00 g/mol) = 98.09 g/mol
Step 2: Determine the mass of H2SO4 in a given volume of solution.
Let's assume we have 100 g of the solution.
Since the solution is 86% by weight, the mass of H2SO4 in 100 g of the solution is:
Mass of H2SO4 = 86% x 100g = 86g
Step 3: Calculate the number of moles of H2SO4.
Number of moles = Mass / Molecular weight
Number of moles of H2SO4 = 86g / 98.09 g/mol = 0.877 mol
Step 4: Calculate the volume of the solution in liters.
To convert from g/cm³ to L, we need to know the density of the solution.
Given that the density of the concentrated sulfuric acid is 1.80 g/cm³, it means that 1 cm³ of the solution weighs 1.80 g.
Volume of the solution = Mass of the solution / Density
Volume of the solution = 100 g / 1.80 g/cm³ = 55.6 cm³
Now, we need to convert cm³ to liters. Since 1 L = 1000 cm³:
Volume of the solution = 55.6 cm³ / 1000 = 0.056 L
Step 5: Calculate the molarity of the solution.
Molarity (M) = moles of solute / volume of solution in liters
Molarity = 0.877 mol / 0.056 L = 15.66 M
Therefore, the molarity of the solution is approximately 15.66 M.
To find the molarity of the solution, we need to understand what molarity is. Molarity is a measure of the concentration of a solute in a solution and is defined as the number of moles of solute per liter of solution.
Step 1: Determine the molar mass of sulfuric acid (H2SO4):
The molar mass of sulfuric acid (H2SO4) is calculated by summing the atomic masses of all its constituent elements. In this case:
Molar mass of sulfur (S) = 32.06 g/mol
Molar mass of oxygen (O) = 16.00 g/mol
Molar mass of hydrogen (H) = 1.01 g/mol
So, the molar mass of sulfuric acid (H2SO4) can be calculated as follows:
(2 × Atomic mass of hydrogen) + Atomic mass of sulfur + (4 × Atomic mass of oxygen) = (2 × 1.01 g/mol) + 32.06 g/mol + (4 × 16.00 g/mol) = 98.09 g/mol
Step 2: Calculate the weight of pure sulfuric acid in the solution:
The concentration of the sulfuric acid solution is given as 86% by weight. This means that 86 g of sulfuric acid is present in every 100 g of solution.
To calculate the weight of sulfuric acid in the solution, we can assume the total weight of the solution to be 100 g. Therefore, the weight of sulfuric acid in the solution is:
(86 g / 100 g) × 100g = 86 g
Step 3: Calculate the moles of sulfuric acid in the solution:
To calculate the moles of sulfuric acid, divide the weight of sulfuric acid by its molar mass:
Moles = Weight of sulfuric acid / Molar mass = 86 g / 98.09 g/mol = 0.876 mol
Step 4: Calculate the volume of the solution in liters:
Since the density of the sulfuric acid solution is given as 1.80 g/cm³, we can assume the density to be the same as the solution's mass-to-volume ratio:
Density = Mass / Volume
Rearranging the equation to solve for the volume:
Volume = Mass / Density = 100 g / (1.80 g/cm³) = 55.56 cm³
Since we need the volume in liters, divide by 1000:
Volume = 55.56 cm³ / 1000 = 0.05556 L
Step 5: Calculate the molarity of the solution:
Molarity (M) = Moles / Volume = 0.876 mol / 0.05556 L ≈ 15.76 M
Therefore, the molarity of the solution is approximately 15.76 M.