To calculate the initial mass of A, we can use the first-order reaction equation:
ln(A₀/A) = -kt
Where A₀ is the initial mass of A, A is the remaining mass of A after a certain time, k is the rate constant, and t is the time.
Given that 2.89g of A remains after 1.04 seconds and the rate constant is 0.0278 S^-1, we can plug in these values into the equation and solve for A₀:
ln(A₀/2.89) = -(0.0278)(1.04)
Now we can solve for A₀ by rearranging the equation:
A₀ = 2.89 * e^(-0.0278 * 1.04)
Calculating this expression will give us the initial mass of A.