02 Worked Examples

© 2013 Pearson Education, Inc.General, Organic, and Biological Chemistry, 4/eKaren C. Timberlake

Sample Problem 2.1 Energy Units

Solution

When 1.0 g of diesel fuel burns in a diesel car engine, 48 000 J are released. What is this energy in calories?

Study Check 2.1

Step 1 State the given and needed quantities.Analyze the Problem

Step 2 Write a plan to convert the given unit to the needed unit.

Step 3 State the equalities and conversion factors.

Step 4 Set up the problem to calculate the needed quantity.

The burning of 1.0 g of coal produces 8.4 kcal. How many kilojoules are produced?


Sample Problem 2.2 Converting from Celsius to Fahrenheit Temperature

Solution

During the winter, the thermostat in a room is set at 21 °C. To what temperature, in Fahrenheit degrees, should you set the thermostat?

In the process of making ice cream, rock salt is added to crushed ice to chill the ice cream mixture. If the temperature drops to what is the temperature in degrees Fahrenheit?

Study Check 2.2


Step 2 Write a temperature equation.

Step 3 Substitute in the known values and calculate the new temperature. In the equation, the values of 1.8 and 32 are exact numbers , which do not affect the number of SFs.


Sample Problem 2.3 Converting from Fahrenheit to Celsius Temperature

Solution

In a type of cancer treatment called thermotherapy , temperatures as high as 113 °F are used to destroy cancer cells. What is that temperature in degrees Celsius?

A child has a temperature of 103.6 °F. What is this temperature on a Celsius thermometer?

Study Check 2.3



Step 3 Substitute in the known values and calculate the new temperature.


Sample Problem 2.4 Converting from Celsius to Kelvin Temperature

Solution

A dermatologist may use cryogenic liquid nitrogen at to remove skin lesions and some skin cancers. What is the temperature, in kelvins, of the liquid nitrogen?

Study Check 2.4



Step 3 Substitute in the known values and calculate the new temperature.

On the planet Mercury, the average night temperature is 13 K, and the average day temperature is 683 K. What are these temperatures in degrees Celsius?


Sample Problem 2.5 Classifying Mixtures

a. Copper is an element, which is a pure substance.b. A chocolate chip cookie does not have a uniform composition, which makes it a heterogeneousmixture.c. The gases oxygen and nitrogen have a uniform composition in Nitrox, which makes it a homogeneousmixture.

Solution

Classify each of the following as a pure substance (element or compound) or as a mixture (homogeneous or heterogeneous):

A salad dressing is prepared with oil, vinegar, and chunks of blue cheese. Is this a homogeneous orheterogeneous mixture?

Study Check 2.5

a. copper wireb. a chocolate chip cookiec. Nitrox, a breathing mixture of oxygen and nitrogen for scuba


Sample Problem 2.6 Physical and Chemical Changes

a. A physical change occurs when the ice cube changes state from solid to liquid.b. A chemical change occurs when an enzyme breaks down lactose into simpler substances.c. A physical change occurs when the size of an object changes.

Solution

Classify each of the following as a physical or chemical change:

a. An ice cube melts to form liquid water.b. An enzyme breaks down the lactose in milk.c. Peppercorns are ground into flakes.

Study Check 2.6

Which of the following are chemical changes?

a. Gas bubbles form when baking powder is mixed with vinegar.b. A log is chopped for firewood.c. A log is burned in a fireplace.


Sample Problem 2.7 Calculating Specific Heat

Solution

What is the specific heat, in cal/g °C, of lead if 13.6 cal will raise the temperature of35.6 g of lead by 12.5 °C?


Step 2 Write the relationship for specific heat. In the relationship for specific heat ( SH ), the quantity of heat is divided by the mass and by the temperature change


Sample Problem 2.7 Calculating Specific Heat

What is the specific heat of sodium metal (J/g °C) if 123 J are needed to raise the temperatureof 4.00 g of sodium by 25.0 °C?

Study Check 2.7

Step 3 Set up the problem to calculate the specific heat. Substitute the quantity of heat, in calories, the mass, in grams, and the temperature change in degrees Celsius, into the relationship for specific heat.

Continued


Sample Problem 2.8 Calculating Heat with an Increase in Temperature

Solution

How many joules are absorbed by 45.2 g of aluminum (Al) if its temperature rises from 12.5 °C to 76.8 °C (see Table 2.8)?


Step 2 Calculate the temperature change The temperature change is the difference between the final and initial temperatures.

Step 3 Write the heat equation.


Sample Problem 2.8 Calculating Heat with an Increase in Temperature

Continued

Some cooking pans have a layer of copper on the bottom. How many kilojoules are needed to raise the temperature of 125 g of copper from 22 °C to 325 °C (see Table 2.8)?

Study Check 2.8

Step 4 Substitute in the given values and solve, making sure units cancel.


Sample Problem 2.9 Energy Content for a Food

Solution

At a fast-food restaurant, a hamburger contains 37 g of carbohydrate, 19 g of fat, and 24 g of protein. What is the energy content for each food type and the total energy content, in kcal? Round off the kilocalories for each food type to the tens place.


Using the energy values for carbohydrate, fat, and protein (see Table 2.9), we can calculate the energy for each type of food.

Step 2 Use the energy value of each food type and calculate the kJ or kcal rounded off to the tens place.


Sample Problem 2.9 Energy Content for a Food

Continued

Step 3 Add the energy for each food type to give the total energy for the food.

Total energy content = 150 kcal + 170 kcal + 100 kcal

= 420 kcal

Study Check 2.9

If you buy the same hamburger as described in Sample Problem 2.9 at a fast-food restaurant in Canada, what is the energy content for each food type and the total energy content, in kJ? Round off the kilojoules for each food type to the tens place.

Documents

02 Worked Examples