Problem 96 - Chemistry: The Central Science

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 part in \(10^{9}\) parts 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 \(1.00 \mathrm{~atm}\) pressure. What mass of \(\mathrm{Ni}(\mathrm{CO})_{4}\) is allowable in a laboratory that is \(54 \mathrm{~m}^{2}\) in area, with a ceiling height of \(3.1 \mathrm{~m}\) ?

Step-by-Step Solution

Answer

The allowable mass of \(\mathrm{Ni}(\mathrm{CO})_{4}\) in the laboratory is 1.16 mg.

Step 1: Calculate the number of moles of gas in the laboratory

First, we need to find the volume of the laboratory. The laboratory has an area of \(54 \mathrm{~m}^2\) and a height of \(3.1 \mathrm{~m}\). Therefore, the volume of the laboratory is: \(V = A\cdot h = (54 \mathrm{~m}^2) (3.1 \mathrm{~m}) = 167.4 \mathrm{~m}^3\) Now, we want to express the volume in liters since we will be using the ideal gas law. There are 1000 liters in 1 cubic meter, so: \(V = 167.4 \mathrm{~m}^{3} \cdot \dfrac{1000 \mathrm{~L}}{1 \mathrm{~m}^{3}} = 167400 \mathrm{~L}\) The ideal gas law is defined by the equation \(PV = nRT\), where \(P\) is the pressure (atm), \(V\) is the volume (L), \(n\) is the number of moles, \(R\) is the ideal gas constant (\(0.0821\dfrac{\mathrm{L}\cdot\mathrm{atm}}{\mathrm{mol}\cdot\mathrm{K}\)), and \(T\) is the temperature (K). We have the volume, pressure, and temperature, so we can solve for the number of moles (\(n\)) in the laboratory: \(1.00 \mathrm{~atm} \cdot 167400 \mathrm{~L} = n \cdot 0.0821\dfrac{\mathrm{L}\cdot\mathrm{atm}}{\mathrm{mol}\cdot\mathrm{K}\ }(297 \mathrm{~K})\)

Step 2: Calculate the number of moles of \(\mathrm{Ni}(\mathrm{CO})_{4}\) allowable in the laboratory

We are given the concentration of nickel carbonyl as 1 part in \(10^9\) parts by volume. We will use this ratio to calculate the number of moles of \(\mathrm{Ni}(\mathrm{CO})_{4}\) allowable in the given volume of the laboratory: \(n_{\mathrm{Ni}(\mathrm{CO})_{4}}=\dfrac{n_{\text{total}}}{10^{9}}\), where \(n_{\text{total}}\) is the total number of moles of gas in the laboratory. Solve for \(n_{\text{total}}\) in the previous equation. \(n_{\text{total}} = \dfrac{1.00 \mathrm{~atm} \cdot 167400 \mathrm{~L}}{0.0821\dfrac{\mathrm{L}\cdot\mathrm{atm}}{\mathrm{mol}\cdot\mathrm{K}\ }(297 \mathrm{~K})} = 6813.26 \mathrm{~mol}\) Now we calculate the number of moles of \(\mathrm{Ni}(\mathrm{CO})_{4}\) allowable, \(n_{\mathrm{Ni}(\mathrm{CO})_{4}}\): \(n_{\mathrm{Ni}(\mathrm{CO})_{4}}=\dfrac{6813.26 \mathrm{~mol}}{10^{9}}=6.81326 \times 10^{-6} \mathrm{~mol}\)

Step 3: Convert the moles of \(\mathrm{Ni}(\mathrm{CO})_{4}\) to mass

Now that we have the number of moles of \(\mathrm{Ni}(\mathrm{CO})_{4}\), we can convert it to mass using the molar mass. The molar mass of \(\mathrm{Ni}(\mathrm{CO})_{4}\) is 28.74 g/mol (nickel) + 4(28.01 g/mol) = 170.30 g/mol (for the carbonyls). Using the molar mass, we can convert the moles of \(\mathrm{Ni}(\mathrm{CO})_{4}\) to mass: \(6.81326 \times 10^{-6} \mathrm{~mol} \cdot \dfrac{170.30 \mathrm{~g}}{1 \mathrm{~mol}} = 1.16 \times 10^{-3} \mathrm{~g}\) Thus, the allowable mass of \(\mathrm{Ni}(\mathrm{CO})_{4}\) in the laboratory is 1.16 mg.

Key Concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental principle in Chemistry that explains how gases behave under various conditions of pressure, volume, and temperature. This law is captured by the equation:

• \(PV = nRT\), where
  • \(P\) is the pressure in atmospheres (atm),
  • \(V\) is the volume in liters (L),
  • \(n\) is the number of moles of gas,
  • \(R\) is the ideal gas constant (approximately 0.0821 \(L \, atm/mol \, K\)), and
  • \(T\) is the temperature in Kelvin (K).

To use the Ideal Gas Law, it's important to ensure that all units are consistent, especially the temperature which must be converted from degrees Celsius to Kelvin. In our exercise, the temperature is 24°C. We convert this to Kelvin by adding 273, giving us 297 K.
With these values, the calculation allows for the determination of the amount of gas present in a given volume and under specific conditions, which was crucial for calculating how much nickel carbonyl could safely be present in the laboratory atmosphere.

Nickel Carbonyl

Nickel carbonyl, with the chemical formula \(\text{Ni}(\text{CO})_{4} \), is an extremely toxic compound, often used in the nickel refining process due to its volatility. Its danger stems from both its toxicity and ability to be easily inhaled, making safe handling essential. In laboratories, the maximum allowable concentration of nickel carbonyl is kept exceedingly low, at 1 part per billion (1 part in \(10^9\)).
This is because exposure to even small amounts of nickel carbonyl can result in severe health risks, including respiratory issues and potential carcinogenic effects. Therefore, understanding and calculating the precise allowable quantity in a given space, as we have done in the exercise, is vital for ensuring safety.

• Nickel carbonyl has a molecular structure where a central nickel atom is bonded to four carbon monoxide ligands.
• Its volatility and toxicity demand strict adherence to safety guidelines in environments where it is present.

Molar Mass Calculation

Molar Mass is a key concept in Chemistry that relates to the mass of a given substance (compound or element) divided by the amount of substance. It is expressed in grams per mole (g/mol). To calculate the molar mass, you sum the atomic masses of all atoms present in a molecular formula.
In the case of nickel carbonyl \(\text{Ni}(\text{CO})_{4}\):

• Nickel (Ni) has an atomic mass of approximately 58.69 g/mol.
• The carbon monoxide ligands contribute 4 molecules with carbon and oxygen combining to about 28.01 g/mol each.

Thus, the total molar mass of nickel carbonyl is calculated as follows:
• Nickel: 58.69 g/mol
• 4 Carbon monoxide ligands: \(4 \times 28.01 = 112.04\) g/mol
• Total: \(58.69 + 112.04 = 170.73\) g/mol
This precise value is crucial for translating moles into grams during laboratory calculations, allowing us to determine the allowable mass of nickel carbonyl in a particular space, like in the exercise scenario.