Two elements `A` and `B` combine chemically to from compounds combining with a fixed mass of `A` in I, II and III is `1:3:5`, if 32 parts by mass of `A` combine with 84 parts by mass of `B` in II, then III, 16 parts of `A` will combine with................ by mass of `B`.
(a) 14 parts by mass of Y
(b) 42 parts by mass of Y
(c) 70 parts by mass of Y
(d) 84 parts by mass of Y

Options

A. 14 parts by mass of Y
B. 42 parts by mass of Y
C. 70 parts by mass of Y
D. 84 parts by mass of Y

Answer

To solve the problem, we will follow a systematic approach to find out how many parts by mass of element B combine with 16 parts by mass of element A in the third compound.

### Step 1: Understand the Given Ratios
We know that the compounds formed by elements A and B have a fixed mass ratio of A to B in compounds I, II, and III as 1:3:5. This means:
- For Compound I: \( A:B = 1:x_1 \)
- For Compound II: \( A:B = 1:3 \)
- For Compound III: \( A:B = 1:5 \)

### Step 2: Analyze the Information for Compound II
We are given that 32 parts by mass of A combine with 84 parts by mass of B in Compound II. We can express this as:
- \( \text{Mass of A in II} = 32 \)
- \( \text{Mass of B in II} = 84 \)

### Step 3: Find the Mass of B per Part of A in Compound II
To find how much B combines with a smaller amount of A, we can calculate the mass of B that combines with 16 parts of A:
\[ \text{Mass of B for 16 parts of A} = \left( \frac{84 \text{ parts of B}}{32 \text{ parts of A}} \right) \times 16 \text{ parts of A} \]
Calculating this gives:
\[ \text{Mass of B for 16 parts of A} = \frac{84}{32} \times 16 = 42 \text{ parts of B} \]

### Step 4: Use the Ratio of Compounds to Find Mass of B in Compound III
Now, we need to find out how much B combines with 16 parts of A in Compound III. The ratio of B in Compound II to Compound III is given as \( 3:5 \).

Let \( y \) be the mass of B in Compound III. According to the ratio:
\[ \frac{84}{y} = \frac{3}{5} \]
Cross-multiplying gives:
\[ 3y = 5 \times 84 \]
\[ 3y = 420 \]
\[ y = \frac{420}{3} = 140 \text{ parts of B} \]

### Step 5: Calculate the Mass of B for 16 parts of A in Compound III
Now we can find the mass of B that combines with 16 parts of A in Compound III using the same ratio:
\[ \text{Mass of B in III} = \left( \frac{140 \text{ parts of B}}{32 \text{ parts of A}} \right) \times 16 \text{ parts of A} \]
Calculating this gives:
\[ \text{Mass of B in III} = \frac{140}{32} \times 16 = 70 \text{ parts of B} \]

### Conclusion
Thus, 16 parts of A will combine with **70 parts by mass of B** in Compound III.

### Answer
(c) 70 parts by mass of B

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