Joseph Priestley, a British chemist, was credited with the discovering oxygen in \(1774 .\) In his experiments, he generated oxygen gas by heating \(\mathrm{HgO}(\mathrm{s}) .\) The other product of the decomposition reaction is \(\mathrm{Hg}(1) .\) What volume of wet \(\mathrm{O}_{2}(\mathrm{g})\) is obtained from the decomposition of \(1.0 \mathrm{g} \mathrm{HgO}(\mathrm{s}),\) if the gas is collected over water at \(25^{\circ} \mathrm{C}\) and a barometric pressure of \(756 \mathrm{mmHg} ?\) The vapor pressure of water is \(23.76 \mathrm{mmHg}\) at \(25^{\circ} \mathrm{C}\).

First, determine the molar mass of HgO by adding the atomic masses of Hg and O, which is \(202.59 g/mol + 16.00 g/mol = 218.59 g/mol\).

Next, find the number of moles of HgO in 1g by using the formula \(\frac{mass}{molar\: mass}\). Substituting the given values, we have \(\frac{1g}{218.59g/mol} = 0.00457moles\).

The balanced chemical reaction of the decomposition of HgO is \(2HgO \rightarrow 2Hg + O2\). From the balanced equation, we know that 2 moles of HgO produce 1 mole of O2. Therefore, 0.00457 moles of HgO would produce half as many moles of O2, which is \(0.00457 * 0.5 = 0.002285 moles\).

Use the ideal gas law \(PV = nRT\) to calculate the volume of the gases at the given conditions. Remember the gas is collected over water, so the pressure of the gas will be the barometric pressure minus the vapor pressure of the water. Thus, the pressure of the gas is \(756mmHg - 23.76mmHg = 732.24mmHg\). Converting that to atmospheres gives \(732.24mmHg \times \frac{1atm}{760mmHg} = 0.96374atm\). \(T\) (in Kelvin) here is \(25°C + 273.15 = 298.15K\) and \(R = 0.0821 L.atm/K.mol\). Substituting these values into the ideal gas law equation gives \(V = \frac{nRT}{P} = \frac{0.002285mol \times 0.0821 L.atm/K.mol \times 298.15K}{0.96374atm} = 0.058 L or 58 mL\). So, the collected O2 will occupy 58mL under the given conditions.

The measured volume of O2 is not correct because it contains water vapor. Therefore the volume of dry O2 will be less than 58mL. The correct volume of dry O2 can't be determined without more information, specifically, the vapor pressure of water at the temperature of the gas in the eudiometer (gas collection tube).