The half-life of 13252Te is 3.26 days. This isotope decays by beta emission to a highly unstable intermediate that decays rapidly to a stable product by beta emission.
(a) What is the ultimate product obtained from Te-132? Write a balanced equation for this reaction.
(b) Gaseous H2Te is made with Te-132. When the tellurium isotope decays, the H2Te produces H2 and the ultimate decay product of Te-132. Write a balanced equation for the formation of stable products from H2132Te.
(c) If a pure sample of 0.0117 mol of H2Te made entirely of Te-132 is placed in an evacuated 2.20-L flask, how much H2Te remains after 89.0 h?
If the temperature is 29°C, what is the pressure in the flask?
(a) To determine the ultimate product obtained from Te-132, we need to refer to the periodic table. The element Te-132 undergoes beta decay, meaning it emits a beta particle, or an electron (e-), during the decay process. This decay process converts the element with atomic number 52 (Te-132) into an element with atomic number 53 (I-132). Hence, the ultimate product obtained from Te-132 is iodine-132 (I-132).
The balanced equation for this reaction is:
Te-132 -> I-132 + e-
(b) When H2Te reacts with Te-132 during its decay, it produces H2 (hydrogen gas) and the ultimate decay product of Te-132, which is iodine-132 (I-132).
The balanced equation for this reaction is:
H2Te + Te-132 -> H2 + I-132
(c) To determine how much H2Te remains after 89.0 hours, we need to use the concept of half-life. The half-life of Te-132 is given as 3.26 days, which is approximately 78.24 hours. By dividing the given time (89.0 hours) by the half-life, we can calculate the number of half-lives that have occurred:
Number of half-lives = Time elapsed / Half-life of Te-132
Number of half-lives = 89.0 hours / 78.24 hours = 1.14 (approximately)
Since 1.14 half-lives have occurred, we can calculate the remaining fraction of H2Te using the formula:
Remaining fraction = (1/2)^(Number of half-lives)
Remaining fraction = (1/2)^(1.14)
To find out how much H2Te remains after 89.0 hours, multiply the initial number of moles (0.0117 mol) by the remaining fraction:
Remaining H2Te = Initial moles of H2Te * Remaining fraction
Now, we can determine the pressure in the flask by using the ideal gas equation:
PV = nRT
where:
P = pressure (unknown)
V = volume of the flask (2.20 L)
n = moles of H2Te remaining
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin (29°C = 29 + 273.15 = 302.15 K)
Solving for P:
P = (nRT) / V
Substituting the known values into the equation, you can calculate the pressure in the flask.