Nickel carbonyl, \(\mathrm{Ni}(\mathrm{CO})_{4},\) is one of the most toxic substances known. The present maximum allowable concentration in laboratory air during an 8 -hr workday is \(1 \mathrm{ppb}\) (parts per billion) by volume, which means that there is one mole of \(\mathrm{Ni}(\mathrm{CO})_{4}\) for every \(10^{9}\) moles of gas. Assume \(24^{\circ} \mathrm{C}\) and 101.3 kPa pressure. What mass of \(\mathrm{Ni}(\mathrm{CO})_{4}\) is allowable in a laboratory room that is \(3.5 \mathrm{~m} \times 6.0 \mathrm{~m} \times 2.5 \mathrm{~m} ?\)

The allowable mass of Nickel carbonyl, \(\mathrm{Ni}(\mathrm{CO})_{4}\), in a laboratory room with dimensions \(3.5 \mathrm{~m} \times 6.0 \mathrm{~m} \times 2.5 \mathrm{~m}\) at a temperature of \(24^{\circ} \mathrm{C}\) and pressure of 101.3 kPa is calculated using the following steps: 1. Determine the room's volume (V): \(V = 3.5 \times 6.0 \times 2.5 \mathrm{m}^3\) 2. Convert the volume to liters: \(V(L) = V(\mathrm{m}^3) \times 1000\) 3. Calculate the moles of air (n) in the room using the ideal gas law: \(n = PV / RT\) 4. Determine the moles of \(\mathrm{Ni}(\mathrm{CO})_{4}\) allowed in the room: Moles of \(\mathrm{Ni}(\mathrm{CO})_{4}\) \(= \frac{\text{Total moles of gas}}{10^9}\) 5. Convert the moles of \(\mathrm{Ni}(\mathrm{CO})_{4}\) to mass: Mass of \(\mathrm{Ni}(\mathrm{CO})_{4}\) \(= \text{Moles of} \; \mathrm{Ni}(\mathrm{CO})_{4} \times \text{Molar mass of} \; \mathrm{Ni}(\mathrm{CO})_{4}\) The final result will be the allowable mass of \(\mathrm{Ni}(\mathrm{CO})_{4}\) in the laboratory room.