How much solution could be heated to boiling by the heat evolved by the dissolution of 28.0 g of NaOH? (For the solution, assume a heat capacity of 4.0 J/g⋅∘C,

To calculate how much solution could be heated to boiling by the heat evolved from the dissolution of NaOH, we need to perform several steps.

1. Calculate the heat evolved during the dissolution of NaOH based on its enthalpy of solution. 2. Assume the initial temperature of the solution before heating. 3. Calculate the amount of solution that can be heated using the heat evolved.

Step 1: NaOH's dissolution is exothermic, and its standard enthalpy change of solution (ΔH_sol) is approximately -44.51 kJ/mol. First, we'll convert the mass of NaOH to moles: Mass of NaOH = 28.0 g Molar mass of NaOH = 22.99 (Na) + 15.999 (O) + 1.008 (H) = 39.997 g/mol

Number of moles (n) = Mass / Molar Mass = 28.0 g / 39.997 g/mol ≈ 0.700 moles

Step 2: The heat (q) involved in the dissolution can be calculated using the formula q = n × ΔH_sol, where n is the number of moles and ΔH_sol is the enthalpy change of solution.

q = 0.700 moles × -44.51 kJ/mol × 1000 J/kJ ≈ -31,157 J

(Note that the value is negative because the dissolution is exothermic, meaning heat is released.)

Step 3: Let's assume the initial temperature of the solution is 25 °C, and the boiling point of the solution is 100 °C. The temperature change (ΔT) needed to bring the solution to boiling is: ΔT = 100 °C - 25 °C = 75 °C

We are given a heat capacity (C) of the solution, which is 4.0 J/g°C.

The formula relating heat transferred, mass, specific heat, and temperature change is q = m × C × ΔT, where m is the mass of the solution in grams.

We will rearrange the formula to solve for m: m = q / (C × ΔT)

Substituting the known values: m = -31,157 J / (4.0 J/g°C × 75 °C)

m ≈ -31,157 J / (300 J/g) ≈ -103.857 g

Since we cannot have a negative mass, we take the absolute value as we are interested in how much solution can be heated. So, approximately 103.857 g of solution could be heated to boiling by the heat evolved from the dissolution of 28.0 g of NaOH.