Ch.9 - Thermochemistry: Chemical Energy

Problem 55a

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Chapter 9, Problem 55a

At a constant pressure of 0.905 atm, a chemical reaction takes place in a cylindrical container with a movable piston having a diameter of 40.0 cm. During the reaction, the height of the piston drops by 65.0 cm. (The volume of a cylinder is V=pr2h,wherehistheheight;1Latm=101.3J.) (a) What is the change in volume in liters during the reaction?

Verified step by step guidance

Step 1: Convert the diameter of the cylinder to radius in meters. The radius is half of the diameter. Also, remember to convert the radius from centimeters to meters by dividing by 100.

Step 2: Convert the change in height from centimeters to meters by dividing by 100. This is because the volume of the cylinder is usually calculated in cubic meters.

Step 3: Calculate the change in volume using the formula for the volume of a cylinder, V = πr²h. Here, r is the radius of the cylinder, h is the change in height, and π is a constant approximately equal to 3.14159.

Step 4: Convert the change in volume from cubic meters to liters. 1 cubic meter is equal to 1000 liters.

Step 5: The result from step 4 is the change in volume in liters during the reaction.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Volume of a Cylinder

The volume of a cylinder can be calculated using the formula V = πr²h, where r is the radius and h is the height. In this context, the radius is derived from the diameter of the piston, and the height corresponds to the change in height of the piston during the reaction. Understanding this formula is essential for determining the change in volume as the piston moves.

Pressure-Volume Relationship

In thermodynamics, the relationship between pressure and volume is crucial, especially under constant pressure conditions. According to Boyle's Law, for a given amount of gas at constant temperature, the pressure and volume are inversely related. This principle helps in understanding how the volume change affects the system's behavior during the reaction.

Unit Conversion

In chemistry, it is often necessary to convert between different units of measurement. In this problem, the volume is calculated in cubic centimeters (cm³) and needs to be converted to liters (L), where 1 L = 1000 cm³. Mastery of unit conversion is essential for accurately reporting results and ensuring consistency in calculations.

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Conversion Factors

Related Practice

Assume that the nutritional content of an apple-say, 50 Cal (1 Cal = 1000 cal) - could be used to light a light bulb. For how many minutes would there be light from each of the following? (a) A 100-watt incandescent bulb (1 W = 1 J/s)

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Textbook Question

A reaction inside a cylindrical container with a movable RAN piston causes the volume to change from 12.0 L to 18.0 L while the pressure outside the container remains constant at 0.975 atm. (The volume of a cylinder is V = pr2h, where h is the height; 1 L # atm = 101.325 J.) (a) What is the value in joules of the work w done during the reaction?

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Textbook Question

A reaction inside a cylindrical container with a movable RAN piston causes the volume to change from 12.0 L to 18.0 L while the pressure outside the container remains constant at 0.975 atm. (The volume of a cylinder is V = pr2h, where h is the height; 1 L # atm = 101.325 J.) (b) The diameter of the piston is 17.0 cm. How far does the piston move?

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Textbook Question

At a constant pressure of 0.905 atm, a chemical reaction takes place in a cylindrical container with a movable piston having a diameter of 40.0 cm. During the reaction, the height of the piston drops by 65.0 cm. (The volume of a cylinder is V=pr2h,wherehistheheight;1Latm=101.3J.) (b) What is the value in joules of the work w done during the reaction?

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Textbook Question

When a sample of a hydrocarbon fuel is ignited and burned in oxygen, the internal energy decreases by 7.20 kJ. If 5670 J of heat were transferred to the surroundings, what is the sign and magnitude of work? If the reaction took place in an environ- ment with a pressure of 1 atm, what was the volume change?

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Textbook Question

What is the difference between the internal energy change ∆E and the enthalpy change ∆H? Which of the two is mea- sured at constant pressure and which at constant volume?

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