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Chapter 6: Problem 49

A particular coal sample contains \(3.28 \%\) S by mass. When the coal is burned, the sulfur is converted to \(\mathrm{SO}_{2}(\mathrm{g}) .\) What volume of \(\mathrm{SO}_{2}(\mathrm{g}),\) measured at \(23^{\circ} \mathrm{C}\) and \(738 \mathrm{mm} \mathrm{Hg},\) is produced by burning \(1.2 \times 10^{6} \mathrm{kg}\) of this coal?

Short Answer

Expert verified
The volume of SO2 produced by burning 1.2 x 10^6 kg of this coal under the given conditions is calculated using the steps above.

Step by step solution

01

Calculate the S mass in kg

First, we need to calculate the mass of sulfur in the coal. This is done by multiplying the total mass of the coal (1.2 x 10^6 kg) by the percentage of sulfur (3.28%) divided by 100. That is: \( S_{mass} = Coal_{mass} * S_{\%} / 100 \). Remember to convert the percentage to a decimal by dividing by 100.
02

Convert S mass to moles of S

By using the molar mass of sulfur (S), we can convert the mass of sulfur calculated in step 1 to moles. The molar mass of S is approximately 32.066 g/mol but our mass is in kg so the molar mass becomes 32.066 kg/kmol. The conversion is done using the formula: \( S_{moles} = S_{mass} / S_{molar mass} \). This gives the amount of moles of sulfur.
03

Convert moles of S to moles of SO2

Now we will convert moles of sulfur to moles of sulfur dioxide (SO2). According to the chemical equation of the burning process, one mole of S is converted to one mole of SO2. Therefore the amount of moles of sulfur dioxide is the same as the amount of moles of sulfur.
04

Convert the given temperature and pressure

Before proceeding with the calculation of the volume, we need to convert the given temperature T (23°C) to an absolute temperature in Kelvin (K): \(T(K) = T(°C) + 273.15 \). Also, convert the pressure given in mmHg to atmospheres (atm) using the conversion factor \(1 atm = 760 mmHg\). The formula to use is: \( P(atm) = P(mmHg) / 760 \).
05

Calculate the volume of SO2

Finally, we can use the ideal gas law equation to calculate the volume of the SO2. The ideal gas law is stated as \(PV = nRT\), where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the absolute temperature. For this problem, we know the value of n from step 3, P from the given pressure, and T from step 4. Also, R is 0.0821 L.atm/K.mol. Rearranging the ideal gas law equation to solve for V, we get: \( V = nRT / P \). Now, all that is left is to substitute the known values into the equation and calculate.

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Most popular questions from this chapter

According to the CRC Handbook of Chemistry and Physics (83rd ed.), the molar volume of \(\mathrm{O}_{2}(\mathrm{g})\) is \(0.2168 \mathrm{Lmol}^{-1}\) at \(280 \mathrm{K}\) and \(10 \mathrm{MPa}\). (Note: \(1 \mathrm{MPa}=\) \(\left.1 \times 10^{6} \mathrm{Pa} .\right)\)(a) Use the van der Waals equation to calculate the pressure of one mole of \(\mathrm{O}_{2}(\mathrm{g})\) at \(280 \mathrm{K}\) if the volume is 0.2168 L. What is the \% error in the calculated pressure? The van der Waals constants are \(a=1.382 \mathrm{L}^{2}\) bar \(\mathrm{mol}^{-2}\) and \(b=0.0319 \mathrm{L} \mathrm{mol}^{-1}\) (b) Use the ideal gas equation to calculate the volume of one mole of \(\mathrm{O}_{2}(\mathrm{g})\) at \(280 \mathrm{K}\) and \(10 \mathrm{MPa}\). What is the \% error in the calculated volume?

A sample of \(\mathrm{O}_{2}(\mathrm{g})\) is collected over water at \(24^{\circ} \mathrm{C}\) The volume of gas is 1.16 L. In a subsequent experiment, it is determined that the mass of \(\mathrm{O}_{2}\) present is 1.46 g. What must have been the barometric pressure at the time the gas was collected? (Vapor pressure of water \(=22.4 \text { Torr. })\)

The Haber process is the principal method for fixing nitrogen (converting \(\mathrm{N}_{2}\) to nitrogen compounds). $$\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{g})$$ Assume that the reactant gases are completely converted to \(\mathrm{NH}_{3}(\mathrm{g})\) and that the gases behave ideally. (a) What volume of \(\mathrm{NH}_{3}(\mathrm{g})\) can be produced from 152 \(\mathrm{L} \mathrm{N}_{2}(\mathrm{g})\) and \(313 \mathrm{L}\) of \(\mathrm{H}_{2}(\mathrm{g})\) if the gases are measured at \(315^{\circ} \mathrm{C}\) and 5.25 atm? (b) What volume of \(\mathrm{NH}_{3}(\mathrm{g}),\) measured at \(25^{\circ} \mathrm{C}\) and\(727 \mathrm{mmHg},\) can be produced from \(152 \mathrm{L} \mathrm{N}_{2}(\mathrm{g})\) and \(313 \mathrm{L} \mathrm{H}_{2}(\mathrm{g}),\) measured at \(315^{\circ} \mathrm{C}\) and \(5.25 \mathrm{atm} ?\)

A gaseous hydrocarbon weighing \(0.231 \mathrm{g}\) occupies a volume of \(102 \mathrm{mL}\) at \(23^{\circ} \mathrm{C}\) and \(749 \mathrm{mmHg} .\) What is the molar mass of this compound? What conclusion can you draw about its molecular formula?

A 10.0 g sample of a gas has a volume of \(5.25 \mathrm{L}\) at \(25^{\circ} \mathrm{C}\) and \(762 \mathrm{mm} \mathrm{Hg} .\) If \(2.5 \mathrm{g}\) of the same gas is added to this constant 5.25 L volume and the temperature raised to \(62^{\circ} \mathrm{C},\) what is the new gas pressure?
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