# Solutions to General Chemistry (Linus Pauling)/The Nature and Properties of Matter

## 1-1

What is the difference between matter and radiant energy?

The essential distinction between these two forms of mass-energy is that matter moves at a velocity of less than the speed of light, and that radiant energy moves at the speed of light.

## 1-2

What is the Einstein relation between mass and energy? Indicate the IS units of the terms in this relation. This is of course the cliched ${\displaystyle E=mc^{2}}$. In terms of IS units, the equation reads:

${\displaystyle \mathrm {J} =\mathrm {kg} \cdot \left({\frac {\mathrm {m} }{\mathrm {s} }}\right)^{2}}$

Note that the term ${\displaystyle \mathrm {J} }$ (for joules) on the left hand resolves to:

${\displaystyle \mathrm {N} \cdot \mathrm {m} =\mathrm {kg} \cdot {\frac {\mathrm {m} }{\mathrm {s} ^{2}}}\cdot \mathrm {m} =\mathrm {kg} \cdot \left({\frac {\mathrm {m} }{\mathrm {s} }}\right)^{2}}$

As such the units are equal on either side, as required.

## 1-3

Approximately how much energy, in IS units, is needed to raise 1 liter (1 kg) of liquid water from 273.15°K to 373.15°K? (See the discussion of the calorie, Section 1-3.)

The answer will have to be written in joules. However, the most convenient unit for the purposes of calculation is the thermochemical calorie, which is equal to 4.184 J. The thermochemical calorie, in turn, is slightly smaller than the 15°C calorie, the unit of energy required to raise the temperature of a gram of water from 14.5 to 15.5°C at standard temperature. Since only an approximate answer is needed, though, simply bear in mind that the Kelvin and the Celsius scale have the same magnitude. Then the required number of (thermochemical) calories is 100,000 thermochemical calories, or 418,400 joules (418.4 kJ).

## 1-4

Verify the following... To convert celsius to farenheight we must multiply by 1.8 and addition 32, to convert farenheight to celsius we must substract 32 and then divide by 1.8.

## 1-5

Mercury freezes at -40°C. What is its freezing point on the Fahrenheit scale?

-40°F (the only temperature which is the same on both scales).

## 1-6

For each of the following systems systems ([1]) state how many phases are present in the system; ([2]) state for each phase whether it is a pure substance or a mixture; ([3]) give the constituents of the system; ([4]) give a set of components for system:

1. A flask containing a saturated aqueous solution of salt and several crystals of salt.
1. Two.
2. The aqueous phase is a mixture, as it contains water and salt. The solid phase, however, can be considered a pure substance.
3. The constituents are the aqueous and solid phases of salt.
4. The components are salt and water.
2. An evacuated, sealed quartz tube of 100-ml volume containing 10 g of pure zinc heated until about one half the zinc is melted.
1. Disregarding the quartz tube itself, there are two phases present in the system.
2. Both phases exist in the form of pure substances.
3. The constituents are the liquid and solid phases of zinc.
4. There is one component, zinc.
3. As ([2]) , but containing 10 g of a copper-gold alloy instead of 10 g of zinc.
1. There are two phases in the system (using the same assumption regarding the container as before).
2. Both phases are mixtures, specifically, alloys.
3. The constituents are the liquid and solid phases of the copper-gold alloy.
4. There are two components, copper and gold.

## 1-7

What is meant by "intrinsic property" of a substance? Are odor, shape, density, color, weight, taste, luster, area, magnetic susceptibility, and heat capacity intrinsic properties? Which of these are properties that can be quantitatively measured?

An intrinsic property of a substance is one which is not significantly affected by the size of any given amount of the substance, or its state of subdivision. In other words, a mountain of pulverized salt (sodium chloride) shares in common with a baseball-sized salt crystal certain invariant, intrinsic properties, such as density and cleavage. The color of a substance is an important physical property. It is interesting to note that the apparent color of a substance depends upon its state of subdivision: the color becomes lighter as large particles are ground up into smaller ones, because the distance through which the light penetrates before it is reflected back from the interfaces (surfaces) becomes less as the particles become smaller.

Odor, density, color, taste, magnetic susceptibility and heat capacity are intrinsic properties, though odor and color may be somewhat magnified when the material is finely subdivided. Shape, weight and area are not intrinsic, since they depend on the amount of material.

Density, color, weight, area, magnetic susceptibility and heat capacity can be quantitatively measured.