A vessel is filled with a gas at a pressure of 76 cm of mercury at...

From the ideal gas equation, $PV = nRT = \dfrac{m}{M}RT$.

Since the volume $V$ of the vessel and the temperature $T$ remain constant, the pressure of the gas is directly proportional to its mass $m$.

$P \propto m$

$\Rightarrow \dfrac{P_2}{P_1} = \dfrac{m_2}{m_1}$

Given that the mass of the gas is increased by $75\%$, the final mass is:

$m_2 = m_1 + 0.75m_1 = 1.75m_1$

Substituting the values into the pressure relation:

$\dfrac{P_2}{76} = \dfrac{1.75m_1}{m_1}$

$P_2 = 1.75 \times 76 = 133$ cm of Hg.

Answer: 133 cm of mercury