A gas expands from a volume of $1$ dm$^3$ to $1.25$ dm$^3$ under a pressure of $1$ bar. Find the change in internal energy if $150$ J of heat is supplied to the system.

In which of the following processes the internal energy of system remain constant?

Match List I with List II

List I (Buffers)	List II (Applications)
(A) $\text{HCO}_3^{-1} + \text{H}_2\text{CO}_3$	(I) Maintain the pH of blood forms $7.36$ to $7.42$
(B) Phosphates	(II) In Medicine
(C) Sodium Citrate	(III) In Qualitative analysis of basic radicals
(D) $\text{NH}_4\text{Cl} + \text{NH}_4\text{OH}$	(IV) In fertilizers

Choose the correct answer from the options given below:

Find the pH of a solution formed by mixing equal volume of solution of $0.1$ M sodium propionate and $0.1$ molar propionic acid.
(Given The dissociation constant of propionic acid is $1.3 \times 10^{-5}$)