Glauberite is a mineral containing sodium sulphate (M= 142.0) and calcium-sulphate (M=136) only. It is the chief source of sodium sulphate, which is used in making glass. If a 20.00 g sample of glauberite contains 2.88 g of calcium (M = 40), what mass of sodium sulphate can be extracted from 1 ton (1000 kg) of glauberite?

Options

A. 102 kg
B. 510 kg
C. 719 kg
D. 855 kg

Explanation

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the moles of calcium in the sample
Given:
- Mass of calcium in the sample = 2.88 g
- Molar mass of calcium (Ca) = 40 g/mol

Using the formula for moles:
\[ \text{Moles of Ca} = \frac{\text{mass}}{\text{molar mass}} = \frac{2.88 \, \text{g}}{40 \, \text{g/mol}} = 0.072 \, \text{mol} \]

### Step 2: Calculate the mass of calcium sulfate (CaSO4) in the sample
Given:
- Molar mass of calcium sulfate (CaSO4) = 136 g/mol

Using the formula for mass:
\[ \text{Mass of CaSO4} = \text{moles} \times \text{molar mass} = 0.072 \, \text{mol} \times 136 \, \text{g/mol} = 9.792 \, \text{g} \]

### Step 3: Calculate the mass of sodium sulfate (Na2SO4) in the sample
Given:
- Total mass of the sample = 20.00 g

Using the mass of sodium sulfate:
\[ \text{Mass of Na2SO4} = \text{Total mass} - \text{Mass of CaSO4} = 20.00 \, \text{g} - 9.792 \, \text{g} = 10.208 \, \text{g} \]

### Step 4: Calculate the mass of sodium sulfate that can be extracted from 1 ton (1000 kg) of glauberite
First, convert 1 ton to grams:
\[ 1 \, \text{ton} = 1000 \, \text{kg} = 1,000,000 \, \text{g} \]

Now, we find the mass of Na2SO4 in 1,000,000 g of glauberite:
\[ \text{Mass of Na2SO4 from 1 ton} = \left( \frac{\text{Mass of Na2SO4 in 20 g}}{\text{Mass of sample}} \right) \times \text{Total mass} = \left( \frac{10.208 \, \text{g}}{20.00 \, \text{g}} \right) \times 1,000,000 \, \text{g} \]
\[ = 0.5104 \times 1,000,000 = 510.4 \, \text{kg} \]

### Final Answer
The mass of sodium sulfate that can be extracted from 1 ton of glauberite is **510.4 kg**.

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