A $ 10 \%$ solution of nitric acid has a density of $ 1.50 \frac{g}{mL} $. To calculate the pH, it is necessary to first calculate the mass of the solution:
$m_{solution}$ $=$ $\rho_{solution}\;\cdot\;V_{solution} $ $=$ $1.5\cdot 1000$ $=$ $1050\; g $
Then we calculate the mass of $HNO_3$:
$m_{HNO_3}$ $=$ $\frac{\%_{HNO_3}\cdot m_{solution}}{100}$ $=$ $\frac{10\cdot 1050}{100}$ $=$ $105\; g$
Then, we calculate the number of moles of $HNO_3$:
$n_{HNO_3}$ $=$ $\frac{m_{HNO_3}}{M_{HNO_3}}$ $=$ $\frac{105}{63}$ $=$ $1,67\; mol$
Then, we calculate the molarity of $HNO_3$ (before dissociation!):
$[HNO_3]$ $=$ $\frac{n_{HNO_3}}{V_{solution}}$ $=$ $\frac{1.67}{1}$ $=$ $1.67\; \frac{mol}{L}$
Finally, we calculate the pH:
$pH$ $=$ $-log1,67$ $=$ $-0,23$
