Solutions for Radiactivity Questions

Here are some questions related to Radioactivity with their solutions:

Question 1:

8.5J heat flows out into the Surroundings when a sample of a gas contracts 400 mL by an average pressure of 0.5 atm. Calculate the change in energy of the system.

Solution :

Here,

$\Delta V = -400 mL = -0.4L$

$and P = 0.5 atm.$

$w = P \Delta V$

$= -(0.5 atm)(-0.4 L)$

$0.2L atm$

$0.2 \times 101.2 J (\because 1 L atm = 101.2 J)$

$20.26J$

$\text{given that} q = -8.5 J (\because \text{Heat flows out of the system} )$

$\Delta E = q + w$

$-8.5 J + 2.0.26 J \\ 11.76 J$

$\Delta E$ has positive sign. It means energy of the system increases.

Questions 2:

10 moles of oxygen is kept in 5.0 L cylinder at 313 K. Due to sudden leakage through a hole, all the gas escapes into the atmosphere and the cylinder gets empty. If the atmospheric pressure is 1.0 atm, calculate the work done by the gas.

Solution : According to gas equation,

PV = nRT nRT

$V = \dfrac{nRT}{P}$

$\dfrac{(10 ml)(0.082 L atm K^{-1} mol^{-1})(313K)}{1.0 atm}$

$= 256.66 L$

$\text{now} \Delta V = V_f- V_i$

$256.66 L- 5l$

$251.66 L$

$w = -P\Delta V$

$= -(1.0 atm)(251.66 L)$

$-251.66 L atm$

$-251.66 \times 101.3 J$

$-25493.2 J$

$= -25.4932kJ$

The energy change, $\Delta E$ for the reaction:

$2N_2(g) + O_2(g) \to 2N_2O(g)$ is found to be $166 kJ at 25^0C$ . Calculate the value of enthalpy change, $\Delta H$ , at the same temperature.

Solution : For the reaction

$2N_2(g) + O_2(g) \to 2N_2O(g)$

$\Delta n = 2- (2 + 1) = -1 \text{mole}$

According to gas equation,

$P \Delta V = \Delta nRT \\[3mm] = (-1 mol)(8.314 JK^{-1} mol^{-1})(298 K) \\[3mm] -2477.6J \\[3mm] = -2.477 kJ$

We know that,

$\Delta H = \Delta E + P \Delta V \\[3mm] = 166kJ + (-2.477 kJ) \\[3mm] 163.523 kJ \hspace{2mm}mol^{-1}$

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