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Ch.3 - Chemical Reactions and Reaction Stoichiometry
Chapter 3, Problem 113a,b

Hydrogen cyanide, HCN, is a poisonous gas. The lethal dose is approximately 300 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 3.5 × 4.5 × 2.5 m. The density of air at 26 °C is 0.00118 g/cm3. (b) If the HCN is formed by reaction of NaCN with an acid such as H2SO4, what mass of NaCN gives the lethal dose in the room? 2 NaCN(s) + H2SO4(aq) → Na2SO4(aq) + 2 HCN(g)

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1
Calculate the volume of the room in cubic meters by multiplying the dimensions: 3.5 m * 4.5 m * 2.5 m.
Convert the volume from cubic meters to cubic centimeters, knowing that 1 m^3 = 1,000,000 cm^3.
Calculate the mass of air in the room using the density of air (0.00118 g/cm^3) and the volume in cm^3.
Determine the lethal dose of HCN by multiplying the mass of air (in kg) by the lethal dose per kilogram (300 mg/kg).
Convert the lethal dose from milligrams to grams by dividing by 1000, as 1 g = 1000 mg.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molar Mass and Density

Understanding molar mass and density is crucial for converting between mass and volume. The density of a substance, defined as mass per unit volume, allows us to calculate the mass of air in a given volume. In this problem, the density of air is provided, which will be used to find the total mass of air in the laboratory room.
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Volume Calculation

Calculating the volume of the laboratory room is essential for determining how much air is present. The volume is found by multiplying the room's dimensions (length, width, height). This volume will then be used in conjunction with the density of air to find the total mass of air in the room.
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Lethal Dose Calculation

The concept of lethal dose refers to the amount of a substance that can cause death. In this case, the lethal dose of HCN is given in mg per kg of air. By calculating the total mass of air in the room, we can apply the lethal dose ratio to find the total amount of HCN that would be lethal in that specific volume of air.
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Related Practice
Textbook Question

Burning acetylene in oxygen can produce three different carbon-containing products: soot (very fine particles of graphite), CO(g), and CO2(g). (c) Why, when the oxygen supply is adequate, is CO2(g) the predominant carbon-containing product of the combustion of acetylene?

Textbook Question
A 3.50 g of an alloy which contains only lead and tin is dissolvedin hot HNO3. Excess sulfuric acid is added to thissolution and 1.57g of PbSO4(s) is obtained. (b) Assuming allthe lead in the alloy reacted to form PbSO4, what was theamount, in grams, of lead and tin in the alloy respectively?
Textbook Question

Hydrogen cyanide, HCN, is a poisonous gas. The lethal dose is approximately 300 mg HCN per kilogram of air when inhaled. (c) HCN forms when synthetic fibers containing Orlon® or Acrilan ® burn. Acrilan® has an empirical formula of CH2CHCN, so HCN is 50.9% of the formula by mass. A rug measures 3.5 × 4.5 m and contains 850 g of Acrilan® 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.

Textbook Question

The source of oxygen that drives the internal combustion engine in an automobile is air. Air is a mixture of gases, principally N2(79%) and O2(20%). In the cylinder of an automobile engine, nitrogen can react with oxygen to produce nitric oxide gas, NO. As NO is emitted from the tailpipe of the car, it can react with more oxygen to produce nitrogen dioxide gas. (a) Write balanced chemical equations for both reactions.

Textbook Question

The source of oxygen that drives the internal combustion engine in an automobile is air. Air is a mixture of gases, principally N2(79%) and O2(20%). In the cylinder of an automobile engine, nitrogen can react with oxygen to produce nitric oxide gas, NO. As NO is emitted from the tailpipe of the car, it can react with more oxygen to produce nitrogen dioxide gas. (b) Both nitric oxide and nitrogen dioxide are pollutants that can lead to acid rain and global warming; collectively, they are called 'NOx' gases. In 2009, the United States emitted an estimated 19 million tons of nitrogen dioxide into the atmosphere. How many grams of nitrogen dioxide is this?