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Chlorine gas, or \({Cl}_2\), is a diatomic molecule consisting of two chlorine atoms. It is a greenish-yellow gas that is highly poisonous to living organisms when inhaled or consumed. Its molecular weight is about \({70.9}\, \text{g/mol}\). This means that one mole of chlorine gas weighs \({70.9}\, \text{g}\). Chlorine is quite reactive and combines readily with many other elements, especially with sodium to form common table salt.
\({Cl}_2\) is a member of the halogen family and is often used in industrial applications, such as water purification and in the production of paper and cloth. It is crucial to handle chlorine gas with caution due to its toxic properties.
Understanding these properties is important when dealing with calculations involving chlorine gas, as its molecular mass is needed for conversions between mass and moles, especially when using the Ideal Gas Law.

The concept of a mole is central in chemistry, as it is used to quantify substances. One mole is defined as \(6.022 \times 10^{23}\) entities (atoms, molecules, etc.). In our scenario, the number of moles of chlorine gas is calculated using the formula:
\[ n = \frac{m}{M} \]
where \(m\) is the mass in grams and \(M\) is the molar mass in g/mol. This step is crucial as it translates the mass of a substance into an amount of substance in moles which can then be used in further calculations such as applying the Ideal Gas Law.
Understanding how to convert between mass and moles allows us to manipulate and predict the behavior of gases in different conditions. It is especially useful when you are tasked with finding out how much of a substance has changed due to reactions or loss, like with the chlorine gas in this exercise.

Temperature conversion is essential when working with gas laws. The temperature must be in Kelvin because the Kelvin scale provides an absolute reference point, where absolute zero is the lowest achievable temperature. To convert temperatures from Celsius to Kelvin, you use the formula:
\[ T(\text{K}) = T(^{\circ}\text{C}) + 273.15 \]
This conversion is crucial because gas calculations are sensitive to temperature changes, and using the wrong temperature scale can lead to incorrect results.
In our exercise, both initial and new temperatures are converted from Celsius to Kelvin to accurately apply the Ideal Gas Law. This helps in determining the volume of the tank and later, the number of moles of chlorine gas after the temperature and pressure change.

Pressure is a measure of the force exerted by the gas particles against the walls of its container. In the context of gases, pressure is typically measured in Pascals (Pa). High pressure conditions mean more force against the container walls, often resulting from more gas molecules or higher energy (temperature).
In the Ideal Gas Law, pressure plays a critical role. It is represented by \(P\) in the formula:
\[ PV = nRT \]
where \(P\) is the pressure in Pa, \(V\) is the volume in cubic meters, \(n\) is the number of moles, \(R\) is the universal gas constant (8.31 J/mol·K), and \(T\) is the temperature in Kelvin.
Knowing how to measure and manipulate pressure in calculations is essential when predicting the behavior of gases under different conditions. In our scenario, the change in pressure, along with temperature change, helps determine the moles of chlorine gas remaining in the tank.