A gas absorbs $120$ J of heat and expands by $300 \times 10^{-6}\ \text{m}^3$ against a constant external pressure of $2 \times 10^5\ \text{Nm}^{-2}$. What will be the change in internal energy of the system ?

An ideal gas expands from initial volume $5\ \text{dm}^3$ to $15\ \text{dm}^3$ against a constant external pressure of $2$ atm. What is the work done by the gas ?

A weak base is $1.3\%$ dissociated in its aqueous solution. If $K_b$ for weak base is $1.69 \times 10^{-5}$ at $298$ K. Find the concentration of aqueous solution of weak base.

What is the pH of solution containing $5 \times 10^{-4}\ \text{M}\ \text{H}^+$ ion?