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Chapter 6: Problem 99

A mixture of \(1.00 \mathrm{g} \mathrm{H}_{2}\) and \(8.60 \mathrm{g} \mathrm{O}_{2}\) is introduced into a 1.500 L flask at \(25^{\circ} \mathrm{C}\). When the mixture is ignited, an explosive reaction occurs in which water is the only product. What is the total gas pressure when the flask is returned to \(25^{\circ} \mathrm{C} ?\) (The vapor pressure of water at \(25^{\circ} \mathrm{C}\) is \(23.8 \mathrm{mmHg}\).)

Short Answer

Expert verified
The total gas pressure in the flask at the end of the reaction is approximately \(1.888 atm\).

Step by step solution

01

Balanced Chemical equation

From the statement, Hydrogen (\(H_{2}\)) reacts with Oxygen (\(O_{2}\)) to form water (\(H_{2}O\)). The balanced equation becomes: \(2H_{2} + O_{2} \rightarrow 2H_{2}O\).
02

Find Moles of Reactants

The amount of substance can be calculated using the formula n = m / Mr. Hence, the number of moles for: Hydrogen (\(H_{2}\)) is \(1.00 g / 2.02 g/mol \approx 0.495 mol\) and Oxygen (\(O_{2}\)) is \(8.60 g / 32.00 g/mol \approx 0.269 mol\).
03

Find Moles of Products

From the stoichiometry of the chemical equation, it shows that the amount of \(H_{2}O\) formed is twice the amount of \(H_{2}\) used. Therefore, \(0.495 mol / 2 = 0.2475 mol\) of \(H_{2}O\) vapor is produced. Consequently, \(O_{2} = 0.269 mol - 0.2475 mol = 0.0215 mol\) is unused and remains.
04

Use Ideal Gas Law to find Pressure

The Ideal Gas Law is given by \(PV = nRT\), where P is pressure, V is volume, n is the number of moles, R is the gas constant and T is the temperature in Kelvin. For this calculation, R = 0.0821 Latm/molK and T = 25°C + 273.15 = 298.15 K. Solving for pressure, \(P = nRT/V = (0.0215 mol + 0.2475 mol)(0.0821 Latm/molK)(298.15K) / 1.500 L = 1.919 atm\).
05

Subtract Water Vapor Pressure

The total pressure earlier calculated includes the pressure due to water vapor. The water vapor pressure must be subtracted from the total pressure to get the final pressure in the flask. The pressure of water vapor at 25°C is given as 23.8 mmHg, which can be converted to atm by using the conversion factor 1 atm = 760 mmHg. Hence, 23.8 mmHg = \(23.8 mmHg / 760 = 0.0313 atm\). The final pressure in the flask will be \(1.919 atm - 0.0313 atm = 1.888 atm\) rounded to three decimal places.

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