Which of the following are true for the first order reaction? t3/4  =  2t1/2  t15/16  =  4t1/2  t15/16  =  3t3/4  t7/8  =  2t3/4

The first order reaction is characterized by the rate of the reaction being directly proportional to the concentration of one reactant. The half-life (t1/2) of a first order reaction is constant and does not depend on the concentration of the reactant.

Let's analyze each of the given statements:

1. t3/4 = 2t1/2: This statement is false. For a first order reaction, the time to reach 75% completion (t3/4) is not twice the half-life (t1/2). The relationship between these two times is given by the equation t = (ln(1/(1-x)))/k, where x is the fraction of completion and k is the rate constant. If we plug in x = 0.5 for t1/2 and x = 0.75 for t3/4, we find that t3/4 is not equal to 2t1/2.

2. t15/16 = 4t1/2: This statement is false. Using the same equation as above, if we plug in x = 0.5 for t1/2 and x = 15/16 for t15/16, we find that t15/16 is not equal to 4t1/2.

3. t15/16 = 3t3/4: This statement is false. Again using the same equation, if we plug in x = 0.75 for t3/4 and x = 15/16 for t15/16, we find that t15/16 is not equal to 3t3/4.

4. t7/8 = 2t3/4: This statement is false. If we plug in x = 0.75 for t3/4 and x = 7/8 for t7/8 in the equation, we find that t7/8 is not equal to 2t3/4.

So, none of the given statements are true for a first order reaction.