Question

A drum used to transport crude oil has a volume of \(162 \mathrm{~L}\). How many grams of water, as steam, are required to fill the drum at 1.00 atm and \(108^{\circ} \mathrm{C}\) ? When the temperature in the drum is decreased to \(25^{\circ} \mathrm{C}\), all the steam condenses. How many \(\mathrm{mL}\) of water \((d=1.00 \mathrm{~g} / \mathrm{mL})\) can be collected?

Short answer

Answer: Approximately 114.96 mL of water can be collected when the steam condenses to 25°C.

Step-by-step solution

Convert the given volume of the drum to SI units

First, we need to convert the volume of the drum given in liters to cubic meters (SI units) to use in the Ideal Gas Law equation. 1 L = 0.001 m³ 162 L * 0.001 = 0.162 m³ The volume of the drum is 0.162 m³.

Apply the Ideal Gas Law to find moles of water vapor

We will use PV = nRT to find the number of moles of water vapor (n). The given temperature is in Celsius, so we need to convert it to Kelvin (K). T = 108°C + 273.15 = 381.15 K We are given the pressure as 1.00 atm, which we need to convert to Pascals (Pa). 1.00 atm = 101325 Pa Now, let's input the values into the Ideal Gas Law equation: PV = nRT (101325 Pa)(0.162 m³) = n(8.314 J/(mol·K))(381.15 K) Solve for n: n = (101325 * 0.162) / (8.314 * 381.15) ≈ 6.382 mol

Find grams of water vapor

Now that we have the moles of water vapor, we can use the molecular weight of water (H₂O) to find the mass in grams: Molecular weight of water = 18.015 g/mol grams of water vapor = moles * molecular weight grams of water vapor = 6.382 mol * 18.015 g/mol ≈ 114.96 g There are approximately 114.96 grams of water in the form of steam required to fill the drum.

Find volume of condensed water

When the steam condenses, its volume will be different. To find the volume of condensed water, we will use the given density (d=1.00g/mL). Apply the density formula: d = m / V 1.00 g/mL = 114.96 g / V Solve for V: V = 114.96 g / 1.00 g/mL ≈ 114.96 mL When the temperature in the drum decreases to 25°C, around 114.96 mL of water can be collected after all the steam condenses.