A gas is contained in a vessel and connected to a simple barometer. The atmospheric pressure is 760 mmHg. The mercury level in the open arm of the barometer is 76 cm, and in the arm connected to the g

• Atmospheric pressure $P_{atm} = 760 \text{ mmHg}$.
• Height of mercury in the arm open to the atmosphere (left arm) $h_{atm} = 76 \text{ cm}$.
• Height of mercury in the arm connected to the gas (right arm) $h_{gas} = 82 \text{ cm}$.

• $h_{atm} = 76 \text{ cm} = 760 \text{ mm}$.
• $h_{gas} = 82 \text{ cm} = 820 \text{ mm}$.

The difference in height $\Delta h$ is the absolute difference between the two mercury levels.

Since the mercury level in the arm connected to the gas ($h_{gas}$) is higher than the level in the arm open to the atmosphere ($h_{atm}$), it indicates that the pressure of the gas ($P_{gas}$) is less than the atmospheric pressure ($P_{atm}$). The gas pressure is equal to the atmospheric pressure minus the pressure exerted by the column of mercury of height $\Delta h$.

A. $766 \text{ mmHg}$
B. $754 \text{ mmHg}$
C. $700 \text{ mmHg}$
D. $820 \text{ mmHg}$

The calculated gas pressure matches option C.

The final answer is $\boxed{\text{C. } 700 \text{ mmHg}}$.