For the first-order decomposition, the equation is: ln(x0 / x) = kt. At t = 200, x = 0.0300 M, we have ln(x0 / 0.03) = 200k. At t = 400, when x = 0.0200 M, we utilize ln(x0 / 0.02) = 400k. By multiplying the first equation by 2, we get 2ln(x0 / 0.03) = 400k, which aligns with the second equation, leading us to conclude that 2ln(x0 / 0.03) = ln(x0 / 0.02). This suggests (x0 / 0.03)^2 = x0 / 0.02, allowing us to find x0 = 0.045 M as the initial concentration. Plugging this back into the first equation yields: ln(0.045 / 0.03) = 200k, from which it follows that k = 0.0020273 (rate constant). The half-life can be calculated with x = 0.5x0: ln(x0 / 0.5x0) = 0.0020273t, resulting in ln(2) = 0.0020273t, which simplifies to t = 341.90 minutes (half-life).
Boyle's law describes the relationship between gas pressure and volume.
It asserts that at a constant temperature, pressure is inversely proportional to gas volume.
PV = k
where P represents pressure, V denotes volume, and k is a constant.
P1V1 = P2V2
where the parameters for the initial condition are on the left, and the parameters for the second condition appear on the right side of the formula.
By substituting values into the equation: 4.00 atm x 500 L = 8.0 atm x V
V calculates to 250 L.
Thus, the new volume becomes 250 L.