A catalyst is a substance that decrease the activation energy needed to start a reaction.
Answer : The time passed in years is 
Explanation :
Half-life = 5730 years
First we have to calculate the rate constant, we use the formula :



Now we have to calculate the time passed.
Expression for rate law for first order kinetics is given by:

where,
k = rate constant = 
t = time passed by the sample = ?
a = let initial amount of the reactant = X g
a - x = amount left after decay process = 
Now put all the given values in above equation, we get


Therefore, the time passed in years is 
V1/T1 = V2/T2
V1 = 350. mL
T1 = 25 + 273 = 298 K
V2 = 250. mL
T2 = ?
Solve the equation for T2: T2 = V2T1/V1 = (250. mL)(298 K)/(350. mL) = 213 K = -60°C