   Chapter 12, Problem 72AP

Chapter
Section
Textbook Problem

Two moles of molecular hydrogen (H2) react with 1 mole of molecular oxygen (O2) to produce 2 moles of water (H2O) together with an energy release of 241.8 y/mole of water. Suppose a spherical vessel of radius 0.500 m contains 14.4 moles of H2 and 7.2 moles of O2 at 20.0°C. (a) What is the initial pressure in the vessel? (b) What is the initial internal energy of the gas? (c) Suppose a spark ignites the mixture and the gases burn completely into water vapor. How much energy is produced? (d) Find the temperature and pressure of the steam, assuming it’s an ideal gas. (e) Find the mass of steam and then calculate the steam’s density. (f) If a small hole were put in the sphere, what would be the initial exhaust velocity of the exhausted steam if spewed out into a vacuum? (Use Bernoulli’s equation.)

(a)

To determine
The initial pressure in the vessel.

Explanation

Section1:

To determine: The constant volume occupied by the gas.

Answer: The volume of the gas is 0.524m3 .

Explanation:

Given Info:

The radius of the spherical vessel is 0.500m .

Formula to calculate the volume of the gas is,

V=43πr3

• r is the radius of the vessel

Substitute 0.500m for r to find the volume.

VSun=43π(0.500m)3=0.524m3

Thus, volume of the gas is 0.524m3 .

Conclusion:

From section 1,

The volume of the gas is 0.524m3

The amount of hydrogen in the container is 14.4mol .

The amount of oxygen in the container is 7.2mol .

The initial temperature is 20°C

To find the initial pressure of the vessel, consider the components in the gas mixture in container as ideal gases. Hence, the total pressure the mixture exerts on the container will be the sum of pressure of the components of the mixture

The pressure exerted by the hydrogen molecule is,

PH2=nH2RTV (I)

• nH2 is the amount of hydrogen molecules in moles
• R is the universal gas constant
• T is the absolute temperature
• V is the volume of the container

The pressure exerted by the oxygen molecule is,

PO2=nO2RTV (II)

• nO2 is the amount of oxygen molecule in moles

The total pressure exerted on the container is the sum of equation (I) and (II)

(b)

To determine
The initial internal energy of the gas.

(c)

To determine
The energy produced if the gas burns out to water vapor completely.

(d)

To determine
The temperature and pressure of the steam.

(e)

To determine
The mass of steam and steam’s density.

(f)

To determine
The initial exhaust velocity of the exhaust steam.

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