I posted this before and am sorry to post again and take up room but it is due this week and I'd like to understand how to get the answer (no one has responded yet):
question
The nuclide 38cl decays by beta emission with a half life of 40min. A sample of .40 m of H38cl is placed in a 6.24 liter container. After 80 min the pressure is 1650 mmHg. What is temperature of container?
I have tried calculating the decay rate of the 38cl and then plugging into the formula pv =nrt but I do not get the answer, 300 k. Any help would be great.
I would think it would be like this:
.40 mol is .0258% Hydrogen
.40 mole is .974 CL38
.40 x .974=.3896 x half life .25=.0974 + mole of hydrogen .01032
=.1077
13.54/.1077= 125k but this isn't correct
The correct answer is 300K
anybody know how it was obtained?
I'm responding just to let you know that I've looked at the problem more than once over the last day or two. Is the HCl a gas? I suppose no if it is a 0.40 m solution. Is that m and not M? How much of the 0.40m solution? is used? The problem doesn't say. And do you realize that Cl38 goes to Ar38 upon releasing a beta particle.
I got the correct answer on this problem. The problem you are having is with the partial pressures. You have .400 mol H38Cl at the start. The 38Cl undergoes 2 half lives to .100 mol. So now in the solution you have left .100 mol of H38Cl. The H gas that falls off of this would become H2 gas in that state. So you have .300 mol H fall off of the H38Cl. That combines to be .150 mol H2. The beta decay of the 38Cl resulted in .300 mol 38Ar. The remaining amounts gives you .55 mol of gas. Apply that to PV=nRT. Don't screw up the units.
To solve this problem, you need to combine the concepts of radioactive decay and ideal gas law.
Step 1: Calculate the decay rate of 38Cl.
The half-life of a radioactive substance is the time it takes for half of the substance to decay. In this case, the half-life of 38Cl is given as 40 minutes. So, after 40 minutes, half of the initial amount of 38Cl will decay. After another 40 minutes (total of 80 minutes), another half will decay, and so on.
To calculate the decay rate, you can use the formula:
N = N0 * (1/2)^(t / half-life)
where N is the final number of atoms, N0 is the initial number of atoms, t is the time elapsed, and the half-life is given as 40 minutes.
In this case, the initial number of atoms N0 is 0.40 mol of H38Cl, and the time elapsed is 80 minutes:
N = 0.40 * (1/2)^(80 / 40)
Step 2: Calculate the number of moles of 38Cl left after radioactive decay.
Using the decay rate calculated in the previous step, you can calculate the remaining number of moles of 38Cl:
Remaining moles of 38Cl = Initial moles of 38Cl * decay rate
In this case:
Remaining moles of 38Cl = 0.40 mol * N
Step 3: Calculate the number of moles of H2 gas produced.
Since we know that 1 mol of 38Cl produces 1 mol of H2 gas, the number of moles of H2 gas produced is the same as the remaining moles of 38Cl.
Number of moles of H2 gas = Remaining moles of 38Cl
In this case:
Number of moles of H2 gas = Remaining moles of 38Cl
Step 4: Calculate the pressure of the H2 gas using the ideal gas law.
The ideal gas law is given by the formula:
PV = nRT
where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
In this case, you are given the pressure (1650 mmHg) and the volume (6.24 liters). You have already calculated the number of moles of H2 gas in the previous step. The value of the ideal gas constant, R, is 0.0821 L·atm/(mol·K).
Plug in the values into the ideal gas law formula:
(1650 mmHg)(6.24 L) = (number of moles)(0.0821 L·atm/(mol·K))(temperature)
Solve for temperature:
Temperature = [(1650 mmHg)(6.24 L)] / [(number of moles)(0.0821 L·atm/(mol·K))]
Substitute the value for the number of moles of H2 gas from the previous step:
Temperature = [(1650 mmHg)(6.24 L)] / [(Remaining moles of 38Cl)(0.0821 L·atm/(mol·K))]
Step 5: Convert units and solve.
Convert the pressure from mmHg to atm by dividing by 760:
Temperature = [(1650 mmHg) / (760 mmHg/atm)] * (6.24 L) / [(Remaining moles of 38Cl)(0.0821 L·atm/(mol·K))]
Finally, substitute the value for Remaining moles of 38Cl that you calculated earlier, and solve for Temperature. This will give you the temperature of the container.