1. Engineers design air bags that deploy almost instantly upon impact. To do this, an air bag must provide a large amount of gas in a very short time. Many manufacturers use sodium azide, NaN3, to produce the gas in such a manner

2NaN3(s)  2Na(s) + 3N2(g)

What volume of N2 gas is produced if 117.0g of sodium azide is reacted at 20.2C and 101.2 kPa?

a. How many molecules of N2 are present in this volume? (Use Avogadro’s constant)

b. How many nitrogen atoms are present in this volume?

2. Consider the incomplete combustion reaction that you observed with the butane lighter:

C4H8 + 5O2  3CO2 + 4H20 + C(s)

Assume that the butane is a gas at the time of combustion. Assume that, at SATP, a mass of 0.01 of butane is burned.

a. What mass of solid carbon is produced?
b. How many atoms is this?

3. In a brief statement (about 150 words), describe a situation where knowledge of the idea gas law and stoichiometric calculations are, or may be, used in a technological application. You may do a little research on this matter. It is not critical that you understand the precise mathematics of what you are researching – you just need to explain how knowledge of the laws we’ve discussed would be useful.

1. To find the volume of N2 gas produced, we need to use the ideal gas law equation: PV = nRT. In this equation, P represents the pressure (101.2 kPa), V represents the volume (which is what we need to find), n represents the number of moles of gas, R is the ideal gas constant (0.0821 L·atm/(mol·K)), and T represents the temperature (20.2°C, which needs to be converted to Kelvin).

First, we need to calculate the number of moles of NaN3 reacted. To do this, we divide the given mass of sodium azide (117.0 g) by its molar mass (65.01 g/mol) to get the number of moles (n = 117.0 g / 65.01 g/mol = 1.7982 mol).

Now we can rearrange the ideal gas law equation to solve for V: V = nRT / P. Plugging in the values, we get V = (1.7982 mol) * (0.0821 L·atm/(mol·K)) * (20.2°C + 273.15 K) / (101.2 kPa).

After performing the calculations, we will have the volume of N2 gas produced in liters.

a. To find the number of molecules of N2 gas, we need to use Avogadro's number (6.022 x 10^23 molecules/mol). We can multiply the number of moles of N2 gas by Avogadro's number to get the number of molecules.

b. To find the number of nitrogen atoms, we can multiply the number of molecules of N2 gas (from part a) by 2, as there are 2 nitrogen atoms in each N2 molecule.

2. To find the mass of solid carbon produced in this incomplete combustion reaction, we need to use stoichiometry. From the balanced equation, we can see that the ratio between the moles of C4H8 and moles of C is 1:1. So, if 0.01 mol of C4H8 is burned, we will also produce 0.01 mol of C.

To find the mass of solid carbon, we multiply the moles of C by its molar mass (12.01 g/mol). This will give us the mass of solid carbon produced.

a. To find the number of carbon atoms, we can multiply the moles of C (from part a) by Avogadro's number (6.022 x 10^23 atoms/mol).

3. One real-world application where knowledge of the ideal gas law and stoichiometry are used is in the automotive industry. When designing the fuel injection systems for cars, engineers need to consider the ideal gas law to ensure that the correct amount of fuel is delivered to the engine.

By using the ideal gas law, engineers calculate the volume of the fuel injector and the pressure at which the fuel needs to be injected. This ensures an optimal air-fuel mixture, leading to efficient combustion and improved fuel efficiency.

Furthermore, stoichiometry is involved in determining the correct air-to-fuel ratio for combustion. Engineers need to know the balanced chemical equation for the combustion of the specific fuel being used. With this information, they can calculate the ideal air-to-fuel ratio to achieve complete combustion and minimize harmful emissions.

In summary, knowledge of the ideal gas law and stoichiometry is crucial in designing fuel injection systems and optimizing combustion processes in the automotive industry, helping to improve fuel efficiency and reduce environmental impact.