Answer:
T =76.13 K
Explanation:
Given data:
Temperature of gas = ?
Volume of gas = 250 mL(250/1000 = 0.25 L)
Mass of helium = 0.40 g
Pressure of gas = 253.25 kpa (253.25/101 = 2.5 atm)
Solution:
Formula:
PV = nRT
First of all we will determine the number of moles of helium.
Number of moles = mass/ molar mass
Number of moles = 0.40 g/ 4 g/mol
Number of moles = 0.1 mol
Now we will put the values.
R = general gas constant = 0.0821 atm.L/ mol.K
T = PV/nR
T =2.5 atm× 0.25 L /0.1 mol ×0.0821 atm.L/ mol.K
T = 0.625 /0.00821/K
T =76.13 K
t1/2 = ln 2 / λ = 0.693 / λ
Where t1/2 is the half life of the element and λ is decay constant.
32 = 0.693 / λ
λ = 0.693 / 32 (1)
Nt = Nο eΛ(-λt) (2)
Where Nt is atoms at t time, λ is decay constant and t is the time taken.
t = 1.9 hours = 1.9 x 60 min
From (1) and (2),
Nt = Nο e⁻Λ(0.693/32)*1.9*60
Nt = 0.085Nο
Percentage = (Nt/Nο) x 100%
= (0.085Nο/Nο) x 100%
= 8.5%
Hence, Percentage of remaining atoms with the original sample is 8.5%
You can cross multiply and then get k alone so it would look like this:
76 81
----- = ------ = 76k= 24624
304 k ----- ----------- = k = 324
76 76
so k is equal to 324
hope this helps have a nice day
