Elen `A` and `B` combine to form three different compounds:
`0.3 g of A + 0.4 g of B rarr 0.7 g ` of compound `X`
`18.0 g of A + 48.0 g of B rarr 66.0 g` of compound `Y`
`40.0 g of A + 159.99 g of B rarr 199.99 g` of compound `Z`
Show that the law of multiple proportions is illustrated by the data given above.

Explanation

To demonstrate that the law of multiple proportions is illustrated by the data given, we will analyze the mass ratios of element B that combine with a fixed mass of element A in the three different compounds formed.

### Step-by-Step Solution:

1. **Identify the mass of A and B in each compound:**
- For compound X:
- Mass of A = 0.3 g
- Mass of B = 0.4 g
- For compound Y:
- Mass of A = 18.0 g
- Mass of B = 48.0 g
- For compound Z:
- Mass of A = 40.0 g
- Mass of B = 159.99 g

2. **Calculate the mass of B that combines with 1 g of A for each compound:**
- For compound X:
\[ \text{Mass of B per 1 g of A} = \frac{0.4 \, \text{g}}{0.3 \, \text{g}} = \frac{4}{3} \approx 1.33 \, \text{g} \]
- For compound Y:
\[ \text{Mass of B per 1 g of A} = \frac{48.0 \, \text{g}}{18.0 \, \text{g}} = \frac{48}{18} = \frac{8}{3} \approx 2.67 \, \text{g} \]
- For compound Z:
\[ \text{Mass of B per 1 g of A} = \frac{159.99 \, \text{g}}{40.0 \, \text{g}} = \frac{159.99}{40} \approx 4.00 \, \text{g} \]

3. **List the calculated ratios:**
- Compound X: 1.33 g of B
- Compound Y: 2.67 g of B
- Compound Z: 4.00 g of B

4. **Express the ratios of the masses of B that combine with 1 g of A:**
- The ratios of the masses of B for compounds X, Y, and Z can be expressed as:
\[ 1.33 : 2.67 : 4.00 \]

5. **Convert the ratios to a simpler form:**
- To simplify the ratios, we can divide each value by 1.33:
\[ \frac{1.33}{1.33} : \frac{2.67}{1.33} : \frac{4.00}{1.33} \approx 1 : 2 : 3 \]

6. **Conclusion:**
- The mass ratios of B that combine with a fixed mass of A in the three compounds (1:2:3) illustrate the law of multiple proportions, which states that when two elements combine to form different compounds, the ratios of the masses of one element that combine with a fixed mass of the other element can be expressed in simple whole numbers.