`8.0575xx10^(-2) kg` of Glauber's slat is dissolved in water to obtain `1 dm^(3)` of a solution of density `1077.2 kg m^(-3)`. Calculate the molarity, molality and mole fraction of `Na_(2)SO_(4)` in solution.

Explanation

To solve the problem, we need to calculate the molarity, molality, and mole fraction of Na₂SO₄ (Glauber's salt) in the solution. Let's break it down step by step.

### Step 1: Determine the Molar Mass of Na₂SO₄·10H₂O
The molar mass of Glauber's salt (Na₂SO₄·10H₂O) can be calculated as follows:
- Na: 23 g/mol × 2 = 46 g/mol
- S: 32 g/mol = 32 g/mol
- O: 16 g/mol × 4 = 64 g/mol
- H₂O: (2 × 1 + 16) g/mol × 10 = 180 g/mol
...