Name of the gas:
The gas produced by the reaction between washing powder and dilute sulphuric acid is carbon dioxide (CO2).

Method of collection of gas:
The gas can be collected using the downward displacement of water method. In this method, a gas jar or a test tube is filled with water and inverted in a water-filled beaker or a trough. The gas produced is then allowed to displace the water in the gas jar, collecting the gas at the top of the jar.

Relative density of the gas:
Carbon dioxide gas is heavier than air. It has a relative density of approximately 1.5 times that of air. This means that carbon dioxide gas tends to settle down and accumulate in low-lying areas.

Solubility of the gas in water:
Carbon dioxide is moderately soluble in water. It dissolves in water to form carbonic acid, which gives a slightly acidic solution. The solubility of carbon dioxide increases with decreasing temperature and increasing pressure.

Reaction of the gas with lime water:
When carbon dioxide gas is passed through lime water (calcium hydroxide solution), a white precipitate of calcium carbonate is formed. The chemical equation for this reaction is as follows:
CO2(g) + Ca(OH)2(aq) → CaCO3(s) + H2O(l)
The white precipitate of calcium carbonate is insoluble in water and gives the appearance of a milky solution. This reaction is used as a test for the presence of carbon dioxide gas.

Explanation:
When washing powder, which contains a compound called sodium carbonate, reacts with dilute sulphuric acid, a chemical reaction occurs. This reaction can be represented by the following equation:
Na2CO3(s) + H2SO4(aq) → Na2SO4(aq) + CO2(g) + H2O(l)
In this reaction, sodium carbonate reacts with sulphuric acid to produce sodium sulphate, carbon dioxide gas, and water.

The carbon dioxide gas produced is collected using the downward displacement of water method. The gas, being heavier than air, displaces the water in the gas jar and fills up the space at the top of the jar.

When carbon dioxide gas is passed through lime water, it reacts with calcium hydroxide (present in lime water) to form calcium carbonate, which is insoluble in water. This reaction results in the formation of a white precipitate, giving the appearance of a milky solution.

Overall, the reaction between washing powder and dilute sulphuric acid generates carbon dioxide gas, which can be collected using the downward displacement of water method. The gas is heavier than air, moderately soluble in water, and when passed through lime water, it forms a white precipitate of calcium carbonate.