Question

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 \(3.5 \mathrm{~m} \times 6.0 \mathrm{~m} \times 2.5 \mathrm{~m} ?\)

Short answer

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.

Step-by-step solution

Calculate the total volume of the room.

The given dimensions of the room are: Length = 3.5 m Width = 6.0 m Height = 2.5 m The total volume of the room (in m³) can be calculated by multiplying the three dimensions: Volume = Length × Width × Height

Convert the volume to liters.

To convert the volume from m³ to liters, we will multiply by 1000: Volume (L) = Volume (m³) × 1000

Determine the number of moles of air using the ideal gas law.

The ideal gas law equation is given as: PV = nRT We need to solve for n (moles of air) using the given conditions: P = 101.3 kPa V = Volume (L) (from Step 2) R = 8.314 L･kPa/(K･mol) (gas constant) T = 24 °C + 273.15 = 297.15 K Rearranging the equation to solve for n: n = PV / RT

Calculate the moles of \(\mathrm{Ni}(\mathrm{CO})_{4}\) allowed in the room.

One ppb concentration means that there is 1 mole of \(\mathrm{Ni}(\mathrm{CO})_{4}\) for every \(10^9\) moles of gas. To find the moles of \(\mathrm{Ni}(\mathrm{CO})_{4}\) allowed in the room, we will use: Moles of \(\mathrm{Ni}(\mathrm{CO})_{4}\) = Total moles of gas / \(10^9\)

Convert moles of \(\mathrm{Ni}(\mathrm{CO})_{4}\) to mass.

To calculate the mass of \(\mathrm{Ni}(\mathrm{CO})_{4}\), we will multiply the moles of \(\mathrm{Ni}(\mathrm{CO})_{4}\) (from Step 4) by the molar mass of \(\mathrm{Ni}(\mathrm{CO})_{4}\). Molar mass of \(\mathrm{Ni}(\mathrm{CO})_{4}\) = (58.69 + 4(12.01 + 16.00)) g/mol Mass of \(\mathrm{Ni}(\mathrm{CO})_{4}\) = Moles of \(\mathrm{Ni}(\mathrm{CO})_{4}\) × Molar mass of \(\mathrm{Ni}(\mathrm{CO})_{4}\) The result will be the mass of \(\mathrm{Ni}(\mathrm{CO})_{4}\) allowable in the laboratory room.

Key concepts

Nickel carbonyl toxicity

Nickel carbonyl, represented by its chemical formula \((\text{Ni(CO)}_4)\), is known for its high toxicity. Even at very low concentrations, it poses significant health risks. The compound can penetrate through the airways when inhaled, causing acute effects like headaches, dizziness, or in severe cases, respiratory failure. Long-term exposure risks include damage to the lungs, liver, kidneys, or central nervous system. Because of these dangers, exposure to nickel carbonyl needs strict regulation.

For laboratory environments, the maximum allowable concentration is set at just 1 part per billion (ppb) to ensure safety. This value indicates that, out of a billion moles of gas in the air, only one mole is nickel carbonyl. This demonstrates the compound's extreme toxicity and the importance of maintaining safe air quality in workspaces. Being aware of potential nickel carbonyl exposure and understanding the toxicity levels can prevent harmful health effects.

Moles calculation

Understanding moles is crucial in chemistry for quantifying substances. In our exercise, determining the amount of nickel carbonyl in air uses the principle of moles. The mole is a standard unit in chemistry representing a specific number of particles, typically atoms or molecules, which is \(6.022 imes 10^{23}\) particles per mole, known as Avogadro's number.

In the context of gases, we use the ideal gas law equation, \(PV = nRT\), to calculate the number of moles of air. Here, \(P\) represents the pressure, \(V\) is volume, \(n\) signifies the number of moles, \(R\) is the gas constant, and \(T\) is the temperature. The equation allows us to solve for \(n\), the moles of air, by rearranging it to \(n = \frac{PV}{RT}\).

Once we find the total moles of air, we determine the allowable moles of nickel carbonyl by using the 1 ppb concentration guideline. This means for every \(10^9\) moles of air, only 1 mole of nickel carbonyl can be present. It emphasizes the importance of small calculations and precise measurements in dealing with toxic substances.

Gas concentration in air

Gas concentration refers to how much of a particular gas is present within a mixture, often expressed as parts per billion (ppb) or parts per million (ppm). For nickel carbonyl in our exercise, a concentration of 1 ppb is used, indicating its extremely low allowable presence relative to the entire volume of air. This minimal concentration is crucial for ensuring safety in work environments.

Determining gas concentration involves several steps. We first calculate the volume of the space where the gas is present, then convert this volume to allow use in the ideal gas law calculations. Using the ideal gas law, we find the total moles of air and then apply the ppb concentration to determine the specific allowable moles of nickel carbonyl.

By considering the moles calculation alongside the ppb concentration guideline, we can then compute how much of the toxic gas is present in a given volume. This method is essential for maintaining air quality, especially in areas where harmful gases can be introduced. Understanding how to calculate and control gas concentration helps ensure a safe environment, preventing exposure to toxic chemicals like nickel carbonyl.