50cm 3 of hydrogen are sparked with 100cm 3 of oxygen at 110°C and 1atm.

Explanation

The question is about a reaction between hydrogen and oxygen gases, and the residual gas volume after the reaction mixture passes through an alkaline solution of pyrogallol.

First, let's consider the balanced chemical equation for the reaction between hydrogen and oxygen gases:

\(2H_2(g) + O_2(g) \rightarrow 2H_2O(g)\)

From the equation, we can see that 2 moles of hydrogen gas react with 1 mole of oxygen gas to form 2 moles of water vapor. Now let's examine the initial conditions: 50 cm\(^3\) of hydrogen and 100 cm\(^3\) of oxygen at 110\(^{\circ}\)C and 1 atm.

Since the volume ratio of hydrogen to oxygen is 1:2 in the balanced equation, the reaction will consume all 50 cm\(^3\) of hydrogen and half of the 100 cm\(^3\) of oxygen, leaving 50 cm\(^3\) of oxygen unreacted.

Now, let's consider the effect of passing the reaction mixture through an alkaline solution of pyrogallol. Pyrogallol has a strong affinity for oxygen and will absorb the unreacted oxygen gas. Therefore, the residual gas volume after passing through the pyrogallol solution will only consist of the water vapor produced by the reaction.

Since we started with 50 cm\(^3\) of hydrogen, and the balanced equation shows a 1:1 ratio of hydrogen to water vapor, the water vapor produced also has a volume of 50 cm\(^3\). Therefore, the volume of the residual gas is50 cm\(^3\), which corresponds toOption D.