A student added some bromine (reddish orange) in some carbon tertrachloride to a sample of butane in a test tube and placed it in a dark cupboard. When the student removed the test tube it still had the reddish orange colour. When the test tube was left on the table top it was observed that the reddish orange colour gradually faded and white fumes produced.

with the aid of an equation explain clearly why there was a colour fade and the white fumes.

I answered this about 1-1/2 hours after you posted the first time. Look for your post at 5:43

The reaction that occurred when the student added bromine to the butane in the test tube is an example of a redox reaction. In this case, bromine is the oxidizing agent, and butane is the reducing agent.

The equation for the reaction is as follows:
Br2 + C4H10 → C4H9Br + HBr

In this equation, bromine (Br2) reacts with butane (C4H10) to form 1-bromobutane (C4H9Br) and hydrogen bromide (HBr).

The red-orange color observed initially in the test tube is due to the presence of bromine (Br2), which is a liquid and has an orange-red color. When the test tube is left in a dark cupboard, the reaction between bromine and butane occurs, but it may not proceed to completion. This is why the initial reddish-orange color remains in the test tube.

When the test tube is removed from the cupboard and placed on the tabletop, the color gradually fades. This is because the reaction between bromine and butane continues even in the presence of light. The orange-red color of bromine fades as it is consumed in the reaction.

Additionally, the white fumes observed are a result of the formation of hydrogen bromide (HBr) during the reaction. Hydrogen bromide is a colorless gas that is soluble in water vapor in the air. When hydrogen bromide gas is released from the reaction mixture, it reacts with moisture in the air to form white fumes, which are visible as a white cloud or mist.

In summary, the color fade in the test tube is due to the consumption of the red-orange bromine, and the white fumes are formed as a result of the production of hydrogen bromide gas.