Question

Hydrogen cyanide, HCN, is a poisonous gas. The lethal dose is approximately \(300 \mathrm{mg}\) HCN per kilogram of air when inhaled. (a) Calculate the amount of HCN that gives the lethal dose in a small laboratory room measuring \(12 \times 15 \times 8.0 \mathrm{ft}\). The density of air at \(26^{\circ} \mathrm{C}\) is \(0.00118 \mathrm{~g} / \mathrm{cm}^{3}\). (b) If the \(\mathrm{HCN}\) is formed by reaction of \(\mathrm{NaCN}\) with an acid such as \(\mathrm{H}_{2} \mathrm{SO}_{4}\), what mass of \(\mathrm{NaCN}\) gives the lethal dose in the room? \(2 \mathrm{NaCN}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)+2 \mathrm{HCN}(g)\) (c) HCN forms when synthetic fibers containing Orlon \(^{\oplus}\) or Acrilan \(^{\otimes}\) burn. Acrilan \(^{\oplus}\) has an empirical formula of \(\mathrm{CH}_{2} \mathrm{CHCN},\) so \(\mathrm{HCN}\) is \(50.9 \%\) of the formula by mass. \(\mathrm{A}\) rug measures \(12 \times 15 \mathrm{ft}\) and contains 30 oz of Acrilan \(^{\otimes}\) fibers per square yard of carpet. If the rug burns, will a lethal dose of HCN be generated in the room? Assume that the yield of HCN from the fibers is \(20 \%\) and that the carpet is \(50 \%\) consumed.

Short answer

The lethal dose of Hydrogen Cyanide (HCN) in the small laboratory room is calculated to be \(m_\mathrm{HCN}\). To produce this lethal dose, a mass of NaCN is required, which is calculated using the balanced chemical equation. Burning the Acrilan rug generates an amount of HCN, considering the yield and consumption. Comparing this generated HCN to the lethal dose determines if the burning of the rug could produce a lethal dose of HCN in the room.

Step-by-step solution

Calculate the volume of the laboratory room

To calculate the volume, use the given dimensions: \(12 \times 15 \times 8.0 \mathrm{ft}\). Convert these dimensions from feet to centimeters. Note that there are 30.48 centimeters in one foot. \[V_\text{room} = 12\text{ ft} \times 15\text{ ft} \times 8.0\text{ ft} \times \left(\frac{30.48\text{ cm}}{1\text{ ft}}\right)^3\]

Calculate the mass of air in the room

To find the mass of air in the room, use the volume of the room and the given density of air at \(26^{\circ} \mathrm{C}\). \[m_\text{air} = V_\text{room} \times 0.00118 \frac{\text{g}}{\text{cm}^3}\]

Calculate the lethal dose of HCN in the room

To find the lethal dose of HCN, multiply the mass of air by the lethal dose per kilogram of air: \[m_\mathrm{HCN} = m_\text{air} \times \frac{300\text{ mg HCN}}{1\text{ kg air}}\]

Calculate the mass of NaCN required to form the lethal dose of HCN

Using the balanced chemical equation, find the molar ratio between NaCN and HCN: \[2 \mathrm{NaCN}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)+2 \mathrm{HCN}(g)\] Using this ratio, calculate the mass of NaCN required to form the lethal dose of HCN. Remember to convert HCN mass to moles and use the molar mass of NaCN to find its mass.

Calculate the amount of HCN generated by burning the rug

First, find the total mass of Acrilan fibers in the rug, using the fiber amount per square yard and the rug area. Next, find the mass of HCN in the Acrilan fibers using the given percentage composition of HCN (50.9%). Finally, calculate the amount of HCN generated by burning the rug by considering the given conditions: assume 20% HCN yield and 50% rug consumption.

Compare the generated HCN with the lethal dose

The final step is to compare the calculated amount of HCN generated by burning the rug to the lethal dose calculated in step 3. If the amount of generated HCN is equal to or greater than the lethal dose, then a lethal dose will be produced in the room when the rug burns.

Key concepts

Lethal Dose Calculation

When dealing with hydrogen cyanide, knowing how to calculate a lethal dose is crucial for safety. Hydrogen cyanide (HCN) is an extremely poisonous gas, with a lethal dose (LD) of approximately 300 mg per kilogram of air when inhaled. Here’s how you can calculate this dangerous threshold for a given space.

First, we need to find out the volume of the room in question. For instance, if you're faced with a room measuring 12 x 15 x 8 feet, you'll convert these dimensions to centimeters as one foot equals 30.48 centimeters. Volume (V) can be then calculated as: \[ V_{\text{room}} = 12 \times 15 \times 8 \times (30.48)^3 \ \text{cm}^3 \].

Now, calculate the mass of air in the room, because this will be essential in determining how much HCN is lethal. Given the density of air at 26ºC is 0.00118 g/cm³, you can calculate the mass (m) as: \[ m_{\text{air}} = V_{\text{room}} \times 0.00118 \ \text{g/cm}^3 \].

Finally, you multiply the mass of air by the lethal dose per kilogram of air, meaning 300 mg of HCN. This will give you the lethal amount of HCN for that specific room: \[ m_{\mathrm{HCN}} = m_{\text{air}} \times \frac{300\ \text{mg HCN}}{1\ \text{kg air}} \].
This equation helps you determine the amount of HCN the space can accommodate before reaching a dangerous level.

Chemical Reaction of NaCN with Acid

Sodium cyanide (NaCN) reacts with acids to form HCN gas, a critical aspect to consider when assessing its potential danger. Let's break down this chemical reaction and how it applies to safety in environments where HCN generation is a risk.

The balanced chemical equation for the reaction between sodium cyanide and sulfuric acid (H₂SO₄) is: \[ 2 \mathrm{NaCN}(s) + \mathrm{H}_{2} \mathrm{SO}_{4}(aq) \rightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}(aq) + 2 \mathrm{HCN}(g) \].

From this equation, we see that the reaction of two moles of NaCN produces two moles of HCN. This 1:1 molar ratio is vital for converting the lethal dose of HCN calculated previously back into the amount of NaCN needed to produce that dose.

First, convert the lethal mass of HCN from grams to moles using its molar mass. Then, use the molar ratio to find out the needed moles of NaCN. Finally, calculate the mass of NaCN by multiplying by its molar mass.
- Determine the moles of HCN: \[ \text{Moles of HCN} = \frac{m_{\text{HCN}}}{\text{Molar mass of HCN}} \].
- Using the ratio from the equation, find the moles of NaCN needed.
- Now convert moles of NaCN back to grams using NaCN’s molar mass, to know how much sodium cyanide can produce a lethal dose when reacting with an acid.

HCN Generation from Synthetic Fibers

The combustion of certain synthetic fibers can release hydrogen cyanide gas, important for considering fire safety. Fibers such as Orlon and Acrilan are both known to produce HCN when burned.

Taking Acrilan as an example, its empirical formula is CH₂CHCN, indicating that 50.9% of its mass is HCN. In a practical scenario, imagine a rug with a 12 x 15-foot size made from Acrilan fibers; it contains 30 oz of fibers per square yard. Understanding the potential risk while taking combustion yield and fiber consumption into account is crucial.
- Calculate the rug's area in square yards and multiply by the fibers' weight per yard to find total Acrilan mass.
- Next, calculate the mass of potential HCN: \((\text{Total Acrilan mass}) \times 0.509 \), considering 50.9% mass composition.
- Apply the yield and consumption rates: since the yield of HCN is 20% and rug consumption is 50%, compute total HCN produced as: \((\text{HCN mass}) \times 0.2 \times 0.5 \).
Finally, compare the generated amount of HCN to the lethal dose previously calculated. If it's equal to or greater, it could potentially be deadly in the confined space. Understanding these scenarios helps in environmental preparation and fire safety planning to prevent toxic exposure.