We can find the gas pressure by using a simple proportion.
In fact, if the pressure of the gas was equal to the atmospheric pressure:
[tex]p_a = 1.01 \cdot 10^5 Pa[/tex]
we know that the height in the mercury manometer would have been
[tex]h_a = 773 mm[/tex]
Therefore, if the heigth in the mercury manometer is
[tex]h=63 mm[/tex]
Then the pressure of the gas is given by the following proportion
[tex]h_a : p_a = h: p[/tex]
From which we find
[tex]p= \frac{h p_a}{h_a}= \frac{(63 mm)(1.01 \cdot 10^5 Pa)}{773 mm}=8231 Pa [/tex]
