Explanation:
In order to understand why the statement is false, we need to have a basic understanding of the different speeds associated with a gas and how they relate to each other.

Most Probable Speed
The most probable speed is the speed at which the majority of gas molecules in a sample are moving. It is denoted by the symbol Vp and is given by the expression:

Vp = √(2RT/M)

where R is the ideal gas constant, T is the temperature in Kelvin, and M is the molar mass of the gas.

Root Mean Square Speed
The root mean square speed is the square root of the average of the squares of the speeds of all the gas molecules in a sample. It is denoted by the symbol Vrms and is given by the expression:

Vrms = √(3RT/M)

where R, T, and M have the same meaning as before.

Comparison
Now, let's compare the two speeds mentioned in the statement: the root mean square speed (Vrms) and the most probable speed (Vp). According to the statement, Vrms is 1.128 times greater than Vp.

If we express this mathematically, we get:

Vrms = 1.128 * Vp

Substituting the expressions for Vrms and Vp, we have:

√(3RT/M) = 1.128 * √(2RT/M)

Squaring both sides of the equation, we get:

3RT/M = (1.128)^2 * 2RT/M

Simplifying the equation, we have:

3 = (1.128)^2 * 2

3 = 1.276224 * 2

3 ≈ 2.552448

Since 3 is not approximately equal to 2.552448, the statement is false.

Conclusion
The root mean square speed of a gas is not 1.128 times greater than the most probable speed. Therefore, the correct answer is option 'B': false.