Answer
$$pH =1.466 $$
Work Step by Step
$$Volume = 535 \space mL \times \frac{1 \space L}{1000 \space mL} = 0.535 \space L$$
$$Pressure = 747 \space mmHg \times \frac{1 \space atm}{760 \space mmHg} = 0.983 \space atm$$
$$Temperature/K = 26.5 + 273.15 = 299.7 \space K$$
1. According to the Ideal Gas Law:
$$n = \frac{PV}{RT} = \frac{( 0.983 \space atm )( 0.535 \space L )}{( 0.08206 \space atm \space L \space mol^{-1} \space K^{-1} )( 299.7 \space K)}$$
$$n = 0.0214 \space mol$$
2. Calculate the molarity of the new solution:
$$[HCl] = \frac{0.0214 \space mol}{625 \space mL} \times \frac{1000 \space mL}{1 \space L} = 0.0342 \space M$$
3. Since HCl is a strong acid: $[H_3O^+] = [HCl]$
$$pH = -log[H_3O^+] = -log( 0.0342 ) = 1.466 $$
