Nickel carbonyl, Ni(CO)4, is one of the most toxic substances known. The present maximum allowable concentration in laboratory air during an 8-h workday is 1 ppb (parts per billion) by volume, which means that there is one mole of Ni(CO)4 for every 109 moles of gas. Assume 24°C and 1.00 atm pressure. What mass of Ni(CO)4 is allowable in a laboratory room that is 12ft×20ft×9ft?

Verified step by step guidance

1. Convert the room dimensions from feet to meters to calculate the volume in cubic meters. Use the conversion factor: 1 ft = 0.3048 m.
2. Calculate the volume of the room in cubic meters using the formula: \( \text{Volume} = \text{length} \times \text{width} \times \text{height} \).
3. Use the ideal gas law, \( PV = nRT \), to find the total number of moles of gas in the room. Use \( P = 1.00 \text{ atm} \), \( R = 0.0821 \text{ L atm mol}^{-1} \text{ K}^{-1} \), and convert the temperature to Kelvin.
4. Determine the number of moles of Ni(CO)_4 using the given concentration of 1 ppb, which means 1 mole of Ni(CO)_4 per 10^9 moles of air.
5. Calculate the mass of Ni(CO)_4 using its molar mass (\( M_{\text{Ni(CO)}_4} = 170.73 \text{ g/mol} \)) and the number of moles of Ni(CO)_4 found in the previous step.

Key Concepts

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for calculating the number of moles of gas present in a given volume under specific conditions of temperature and pressure, which is crucial for determining the allowable concentration of nickel carbonyl in the laboratory air.

Concentration Units

Understanding concentration units, such as parts per billion (ppb), is vital for interpreting the question. One ppb indicates that there is one part of a substance in one billion parts of the total mixture, allowing for the conversion of concentration into moles and subsequently into mass, which is necessary for calculating the allowable mass of Ni(CO)4 in the laboratory.

Volume Conversion

To solve the problem, it is important to convert the dimensions of the laboratory room from feet to a volume measurement compatible with the Ideal Gas Law, typically liters or cubic meters. This conversion allows for accurate calculations of the total volume of air in the room, which is needed to determine how much nickel carbonyl can be present at the specified concentration.