The number of moles of $Ca(OH)_2$ required to prepare $250 \ mL$ of solution with $pH$ $14$ (assuming complete ionization) is :-

$50 \ mL$ of $H_2O$ is added to $50 \ mL$ of $1 \times 10^{-3} \ M$ barium hydroxide solution. What is the $pH$ of the resulting solution?

What is the pH of $10^{-8} \ M \ HCl$ solution?

What is the $pH$ of $0.005 \ M \ H_2SO_4$ solution?

$x \ mg$ of $Mg(OH)_2$ (molar mass $= 58 \ g/mol$) is required to be dissolved in $1.0 \ L$ of water to produce a $pH$ of $10.0$ at $298 \ K$. The value of $x$ is $........... mg$ ($Nearest$ $integer$). ($Given$: $Mg(OH)_2$ is assumed to dissociate completely in $H_2O$)

What is the $pH$ of a solution containing $H^{+}$ ion concentration $2.5 \times 10^{-3} \ mol \ dm^{-3}$? (Given $\log 2.5 = 0.3979$)