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Chapter 5: Problem 38

A gas evolved during the fermentation of glucose (wine making) has a volume of \(0.78 \mathrm{~L}\) at \(20.1^{\circ} \mathrm{C}\) and 1.00 atm. What was the volume of this gas at the fermentation temperature of \(36.5^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\) pressure?

Short Answer

Expert verified
The final volume of the gas at the fermentation temperature of \( 36.5^\circ \mathrm{C} \) and \( 1.00 \mathrm{~atm} \) pressure is approximately \( 0.82 \mathrm{~L} \)

Step by step solution

01

Understand Charles's Law and Its Formula

Charles's Law states that the volume of a gas (V) is directly proportional to its absolute temperature (T) when the pressure is held constant. The general formula is \( V1/T1 = V2/T2 \), where V1 and T1 are initial volume and temperature, and V2 and T2 are final volume and temperature.
02

Convert temperatures to Kelvin

In Kelvin, initial temperature T1 is \(20.1^\circ C+273.15 = 293.25 \mathrm{~K} \) and final temperature T2 is \(36.5^\circ C+273.15 = 309.65 \mathrm{~K} \)
03

Substitute the given data into the formula

Substitute the initial volume \( V1=0.78 \mathrm{~L} \), initial temperature \( T1=293.25 \mathrm{~K} \), and final temperature \( T2=309.65 \mathrm{~K} \) into the formula.
04

Solve for the final volume

To find the unknown volume \( V2 \), re-arrange the formula: \( V2 = V1 \times T2/T1 \). And substitute the given value in.

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Most popular questions from this chapter

A sample of air contains only nitrogen and oxygen gases whose partial pressures are 0.80 atm and 0.20 atm, respectively. Calculate the total pressure and the mole fractions of the gases.

The Chemistry in Action essay "Super Cold Atoms" in Section \(5.7 .\) describes the cooling of rubidium vapor to \(5.0 \times 10^{-8} \mathrm{~K}\). Calculate the root-mean-square speed and average kinetic energy of a \(\mathrm{Rb}\) atom at this temperature.

Dry air near sea level has the following composition by volume: \(\mathrm{N}_{2}, 78.08\) percent; \(\mathrm{O}_{2}, 20.94\) percent; Ar, 0.93 percent; \(\mathrm{CO}_{2}, 0.05\) percent. The atmospheric pressure is 1.00 atm. Calculate (a) the partial pressure of each gas in atm and (b) the concentration of each gas in moles per liter at \(0^{\circ} \mathrm{C}\).

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