Ammonia gas diffuses x times faster than hydrogen chloride gas. The value of x is `"________"`.
(Given, molecular masses of ammonia and hydrogen chloride are 17u and 36.5u respectively. )

Explanation

To find out how many times faster ammonia gas diffuses compared to hydrogen chloride gas, we can use Graham's law of effusion. This law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.

### Step-by-Step Solution:

1. **Understand Graham's Law**: According to Graham's law, the rate of diffusion of gas A (R_A) and gas B (R_B) can be expressed as:
\[ \frac{R_A}{R_B} = \sqrt{\frac{M_B}{M_A}} \]
where \(M_A\) and \(M_B\) are the molar masses of gases A and B, respectively.

2. **Identify the Gases and Their Molar Masses**:
- For ammonia (NH₃), the molar mass \(M_{NH3} = 17 \, \text{u}\).
- For hydrogen chloride (HCl), the molar mass \(M_{HCl} = 36.5 \, \text{u}\).

3. **Set Up the Ratio**: We want to find how many times faster ammonia diffuses compared to hydrogen chloride. Thus, we can set:
- \(R_{NH3}\) = rate of diffusion of ammonia
- \(R_{HCl}\) = rate of diffusion of hydrogen chloride

We can express this as:
\[ \frac{R_{NH3}}{R_{HCl}} = \sqrt{\frac{M_{HCl}}{M_{NH3}}} \]

4. **Substitute the Molar Masses**:
\[ \frac{R_{NH3}}{R_{HCl}} = \sqrt{\frac{36.5}{17}} \]

5. **Calculate the Square Root**:
- First, calculate the fraction:
\[ \frac{36.5}{17} = 2.147 \]
- Now take the square root:
\[ \sqrt{2.147} \approx 1.46 \]

6. **Conclusion**: Therefore, ammonia gas diffuses approximately 1.46 times faster than hydrogen chloride gas. Thus, the value of \(x\) is:
\[ x \approx 1.46 \]

### Final Answer:
The value of \(x\) is **1.46**.

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