I posted this before a few hours ago without a reply yet but decided I would add more detail:
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?
To find the temperature of the container, we need to use the Ideal Gas Law equation, which is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
In this case, we want to find the temperature (T). We have the following information:
Pressure (P) = 1650 mmHg
Volume (V) = 6.24 liters
Number of moles (n) = ?
R = 0.0821 L·atm/(mol·K)
To find the number of moles (n), we need to determine the decay rate of 38Cl.
The decay rate can be calculated using the half-life formula:
decay rate = ln(2) / half-life
The half-life of 38Cl is given as 40 min, so the decay rate is:
decay rate = ln(2) / 40
Now we know the decay rate, we can calculate the number of moles (n), which is the amount of hydrogen (H) plus the remaining amount of 38Cl after 80 min:
n = (0.0258 * 0.40) + (0.974 * 0.40 * e^(-decay rate * 80))
where 0.0258 is the molar fraction of hydrogen (H) and 0.974 is the molar fraction of 38Cl.
With the number of moles (n) calculated, we can now rearrange the Ideal Gas Law equation to solve for temperature:
T = PV / (nR)
Substituting the known values, we get:
T = (1650 mmHg * 6.24 L) / (n * 0.0821 L·atm/(mol·K))
Finally, plug in the calculated value of n into the equation and solve for T to get the temperature in kelvin (K).
It is important to note that the approach described above assumes that the gas behaves ideally, and no other factors like non-ideal behavior or chemical reactions are influencing the gas inside the container.