Question

At 600K, the root mean square (rms) speed of gas X (molar mass = 40) is equal to the most probable speed of gas Y at 90K. The molar mass of the gas Y is ____ g mol^-1. (Nearest integer)

Answer 1

Correct Answer: 4

To solve this problem, we need to equate the root mean square (rms) speed of gas X with the most probable speed of gas Y and find the molar mass of gas Y.

Step 1: Understanding Speed Formulas

• The root mean square speed of a gas: \(v_{\text{rms}} = \sqrt{\frac{3RT}{M}}\)
• The most probable speed of a gas: \(v_{\text{mp}} = \sqrt{\frac{2RT}{M}}\)

Step 2: Equating Speeds

• Given that the rms speed of gas X at 600K equals the most probable speed of gas Y at 90K.
• Thus, \(\sqrt{\frac{3RT}{M_X}} = \sqrt{\frac{2RT}{M_Y}}\)

Step 3: Simplifying the Equation

• Square both sides: \(\frac{3RT}{M_X} = \frac{2RT}{M_Y}\)
• Cancel \(R\) and rearrange: \(\frac{3 \times 600}{40} = \frac{2 \times 90}{M_Y}\)

Step 4: Calculating Molar Mass of Gas Y

• Calculate the LHS: \( \frac{3 \times 600}{40} = 45\)
• Solve for \(M_Y\): \(45 = \frac{180}{M_Y}\)
• Thus, \(M_Y = \frac{180}{45} = 4\)

Conclusion

The molar mass of gas Y is \(4\) g mol^-1, which is within the given range of 4 to 4.