Given:
Volume of O2 gas = 100 mL
Time taken for O2 gas to diffuse = 10 s

To find:
Gas X and time t for which 100 mL of gas X diffuses

Solution:
We can use Graham's law of diffusion to solve this problem. According to Graham's law, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.

Mathematically, the equation can be written as:
Rate1 / Rate2 = √(M2 / M1)

Where,
Rate1 and Rate2 are the rates of diffusion of gases 1 and 2, respectively.
M1 and M2 are the molar masses of gases 1 and 2, respectively.

In this case, we need to compare the rate of diffusion of O2 gas (given) with the rate of diffusion of gas X (unknown).

Let's consider O2 gas as gas 1 and gas X as gas 2.

Rate1 = Volume1 / Time1 = 100 mL / 10 s = 10 mL/s

Substituting the given values into the equation, we have:
10 mL/s / Rate2 = √(M2 / M1)

To find the gas X and time t, we need to compare the rates of diffusion of O2 gas and gas X.

Comparing the rates of diffusion:
10 mL/s / Rate2 = √(M2 / M1)

Squaring both sides of the equation, we get:
(10 mL/s / Rate2)^2 = M2 / M1

Simplifying the equation, we have:
100 mL^2 / Rate2^2 = M2 / M1

To determine the gas X and time t, we need to find the gas X for which the rate of diffusion is such that the above equation is satisfied.

Comparing the given answer options:
a) H2, 2.5s
b) SO2, 16s
c) CO, 10s
d) He, 4s

The correct answer is option a) H2, 2.5s because the rate of diffusion of H2 gas is such that it satisfies the equation.

Therefore, gas X is H2 and time t is 2.5 seconds.