Question

73\. The molar heat of vaporization of carbon disulfide, \(\mathrm{CS}_{2},\) is 28.4 \(\mathrm{kJ} / \mathrm{mol}\) at its normal boiling point of 46 \({ }^{\circ} \mathrm{C}\). How much energy (heat) is required to vaporize \(1.0 \mathrm{~g}\) of \(\mathrm{CS}_{2}\) at 46 \({ }^{\circ} \mathrm{C}\) ? How much heat is evolved when \(50 . \mathrm{g}\) of \(\mathrm{CS}_{2}\) is condensed from the vapor to the liquid form at 46 \({ }^{\circ} \mathrm{C}\)?

Short answer

The amount of energy required to vaporize 1.0 g of carbon disulfide (CS₂) at 46°C is 0.372 kJ. The amount of heat released when 50 g of CS₂ is condensed from the vapor to the liquid form at 46°C is 18.6 kJ.

Step-by-step solution

Calculate the molecular weight of CS₂

To do this, we need the atomic weight of carbon (C) and sulfur (S) to find the molecular weight of carbon disulfide (CS₂). The atomic weight of carbon is approximately 12.01 g/mol and that of sulfur is 32.06 g/mol. The molecular weight of CS₂ is: \[12.01 + 2 \times 32.06 = 76.13 \: g/mol\]

Calculate the amount of energy required to vaporize 1.0 g of CS₂

First, we need to find the number of moles of CS₂ in 1.0 g. To do that, divide the mass of CS₂ by its molecular weight: \[\frac{1.0 \: g}{76.13 \: g/mol} = 0.0131 \: mol\] Now, multiply the number of moles by the molar heat of vaporization to find the required energy: \[0.0131 \: mol \times 28.4 \: kJ/mol = 0.372 \: kJ\] Therefore, 0.372 kJ of energy is required to vaporize 1.0 g of CS₂ at 46°C.

Calculate the amount of energy released when 50 g of CS₂ is condensed

First, we need to find the number of moles of CS₂ in 50 g. To do that, divide the mass of CS₂ by its molecular weight: \[\frac{50 \: g}{76.13 \: g/mol} = 0.656 \: mol\] Now, multiply the number of moles by the molar heat of vaporization to find the amount of energy released. Keep in mind that the energy released will be negative since it's an exothermic process (energy is released when condensing from vapor to liquid): \[0.656 \: mol \times -28.4 \: kJ/mol = -18.6 \: kJ\] Therefore, 18.6 kJ of energy is released when 50 g of CS₂ is condensed from the vapor to the liquid form at 46°C.

Key concepts

Molecular Weight Calculation

The molecular weight of a compound is an essential component in various chemical calculations. It's often necessary when converting between grams and moles, which is fundamental to solving many chemistry problems. The molecular weight is the sum of the atomic weights of all atoms in a molecule. For carbon disulfide (\(\mathrm{CS}_2\)), this involves knowing the atomic weights of carbon and sulfur. - **Carbon (C):** approximately 12.01 g/mol - **Sulfur (S):** approximately 32.06 g/mol To find the molecular weight of \(\mathrm{CS}_2\), you add the atomic weight of one carbon atom with twice the atomic weight of sulfur (since \(\mathrm{CS}_2\) contains two sulfur atoms):\[12.01 + 2 \times 32.06 = 76.13 \, \mathrm{g/mol}\]Calculating the molecular weight accurately is crucial, as it allows you to determine how many moles are present in a given sample mass. This step is foundational for subsequent calculations, such as determining energy changes.

Energy Calculation

Energy calculations are integral in understanding the thermal dynamics of chemical reactions. In the context of vaporization, the molar heat of vaporization is the key value; it is the amount of energy required to vaporize one mole of a substance at its boiling point.To find out how much energy is needed to vaporize a certain mass of substance, you'll first need to convert that mass into moles using the molecular weight:- **Number of moles (n):** Divide the mass by molecular weight.For instance, if you have 1.0 g of \(\mathrm{CS}_2\), you find the moles as follows:\[\frac{1.0 \, \mathrm{g}}{76.13 \, \mathrm{g/mol}} = 0.0131 \, \mathrm{mol}\]Next, multiply the number of moles by the molar heat of vaporization to get the energy required:\[0.0131 \, \mathrm{mol} \times 28.4 \, \mathrm{kJ/mol} = 0.372 \, \mathrm{kJ}\]Thus, 0.372 kJ is needed to vaporize 1.0 g of \(\mathrm{CS}_2\). Accurate energy calculations like this are vital for predicting and understanding the energy changes in chemical processes.

Exothermic Process

An exothermic process is one where energy is released, usually in the form of heat. It is a fundamental concept in thermodynamics and reaction energetics. When a substance condenses from a vapor state to a liquid, the process is exothermic.Take the condensation of carbon disulfide as an example. If you start with 50 g of \(\mathrm{CS}_2\), first calculate the moles:\[\frac{50 \, \mathrm{g}}{76.13 \, \mathrm{g/mol}} = 0.656 \, \mathrm{mol}\]Since condensation releases energy, the energy change is negative, reflecting the exothermic nature. Multiply the moles by the negative molar heat of vaporization:\[0.656 \, \mathrm{mol} \times (-28.4 \, \mathrm{kJ/mol}) = -18.6 \, \mathrm{kJ}\]This calculation shows that 18.6 kJ of heat is released as \(\mathrm{CS}_2\) condenses. Recognizing and calculating the energy change in exothermic processes is critical in fields like thermochemistry and engineering.