Extensive property (like volume and mass), can be measured.
Answer:
- m = 1,000/58.5
- b = - 1,000 / 58.5
1) Variables
- molarity: M
- density of the solution: d
- moles of NaCl: n₁
- mass of NaCl: m₁
- molar mass of NaCl: MM₁
- total volume in liters: Vt
- Volume of water in mililiters: V₂
- mass of water: m₂
2) Density of the solution: mass in grams / volume in mililiters
3) Mass of NaCl: m₁
Number of moles = mass in grams / molar mass
⇒ mass in grams = number of moles × molar mass
m₁ = n₁ × MM₁
4) Number of moles of NaCl: n₁
Molarity = number of moles / Volume of solution in liters
M = n₁ / Vt
⇒ n₁ = M × Vt
5) Substitue in the equation of m₁:
m₁ = M × Vt × MM₁
6) Substitute in the equation of density:
d = [M × Vt × MM₁ + m₂] / (1000Vt)
7) Simplify and solve for M
- d = M × Vt × MM₁ / (1000Vt) + m₂/ (1000Vt)
- d = M × MM₁ / (1000) + m₂/ (1000Vt)
Making the simplistic assumption that the dissolved NaCl(s) does not affect the volume of the solvent water means 1000Vt = V₂
- d = M × MM₁ / (1000) + m₂/ V₂
m₂/ V₂ is the density of water: 1.00 g/mL
- d = M × MM₁ / (1000) + 1.00 g/mL
- M × MM₁ / (1000) = d - 1.00 g/mL
- M = [1,000/MM₁] d - 1,000/ MM₁
8) Substituting MM₁ = 58.5 g/mol
- M = [1,000/58.5] d - [1,000/ 58.5]
Comparing with the equation Molarity = m×density + b, you obtain:
- m = 1,000/58.5
- b = - 1,000/58.5
