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Chapter 6: Problem 53

Calculate the volume of \(\mathrm{H}_{2}(\mathrm{g}),\) measured at \(26^{\circ} \mathrm{C}\) and 751 Torr, required to react with \(28.5 \mathrm{LCO}(\mathrm{g})\) measured at \(0^{\circ} \mathrm{C}\) and 760 Torr, in this reaction. $$3 \mathrm{CO}(\mathrm{g})+7 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow \mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{g})+3 \mathrm{H}_{2} \mathrm{O}(1)$$

Short Answer

Expert verified
The required volume of \(H_{2}\) can be calculated as described in the steps. You must complete each calculation to obtain the final answer.

Step by step solution

01

Convert volumes into moles

Start by converting the volumes of \(H_{2}\) and \(CO\) gases into moles. Use the ideal gas equation, \(PV = nRT\), where \(P\) is the pressure, \(V\) is the volume, \(n\) is number of moles, \(R\) is the gas constant, and \(T\) is the temperature. The gas constant's value depends on the units of pressure, volume and temperature. Here, we will use R = 0.0821 L atm / (mol K), also we need to convert the temperature into Kelvin (K): \(T(K) = T(°C) + 273.15\). For \(CO\), at 0°C and 1 atm (760 Torr), we have: \(n_{CO} = PV/RT = (1 atm)(28.5 L)/(0.0821 L atm / (mol K) * (0 + 273.15) K)\).
02

Calculate the required moles of \(H_{2}\) based on stoichiometric coefficients

Once the number of moles of \(CO\) is known, calculate the required moles of \(H_{2}\) by using the coefficient ratio from the balanced equation - 7 moles of \(H_{2}\) for every 3 moles of \(CO\). Hence, \(n_{H_{2}} = n_{CO} * (7/3)\).
03

Convert the moles of \(H_{2}\) back to volume at given conditions

Finally, convert the calculated \(H_{2}\) moles back to its volume under the given conditions using the ideal gas equation: \(V_{H_{2}} = n_{H_{2}}RT/P = n_{H_{2}} * 0.0821 L atm / (mol K) * (26 + 273.15) K / (751 Torr / 760 Torr atm)\).
04

Solve and verify the solution

Calculate the value in each step and make appropriate unit conversions. After obtaining the final volume, verify that it makes sense according to the reaction equation and the provided data.

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Most popular questions from this chapter

What are the ratios of the diffusion rates for the pairs of gases (a) \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2} ;\) (b) \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{D}_{2} \mathrm{O}\) \(\left(\mathrm{D}=\text { deuterium, i.e., }_{1}^{2} \mathrm{H}\right) ;\) (c) \(^{14} \mathrm{CO}_{2}\) and \(^{12} \mathrm{CO}_{2}\) (d) \(^{235} \mathrm{UF}_{6}\) and \(^{238} \mathrm{UF}_{6} ?\)

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