# Solving Real Problems With Chemistry

Representing the Celsius temperature as $$x$$ and the Fahrenheit temperature as $$y$$, the slope, $$m$$, is computed to be: $\begin m &=\dfrac \[4pt] &= \mathrm \[4pt] &= \mathrm \[4pt] &= \mathrm\end$ The y-intercept of the equation, , is then calculated using either of the equivalent temperature pairs, (100 °C, 212 °F) or (0 °C, 32 °F), as: $\begin b&=y-mx \[4pt] &= \mathrm \[4pt] &= \mathrm \end$ The equation relating the temperature scales is then: $\mathrm$ An abbreviated form of this equation that omits the measurement units is: $\mathrm$ Rearrangement of this equation yields the form useful for converting from Fahrenheit to Celsius: $\mathrm$ As mentioned earlier in this chapter, the SI unit of temperature is the kelvin (K).Unlike the Celsius and Fahrenheit scales, the kelvin scale is an absolute temperature scale in which 0 (zero) K corresponds to the lowest temperature that can theoretically be achieved.The space between these two points on a Fahrenheit thermometer is divided into 180 equal parts (degrees).

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The early 19th-century discovery of the relationship between a gas's volume and temperature suggested that the volume of a gas would be zero at −273.15 °C.

In 1848, British physicist William Thompson, who later adopted the title of Lord Kelvin, proposed an absolute temperature scale based on this concept (further treatment of this topic is provided in this text’s chapter on gases).

Note that, just as for numbers, when a unit is divided by an identical unit (in this case, m/m), the result is “1”—or, as commonly phrased, the units “cancel.” These calculations are examples of a versatile mathematical approach known as . are equivalent (by definition), and so a unit conversion factor may be derived from the ratio, $\mathrm$ Several other commonly used conversion factors are given in Table $$\Page Index$$.

When we multiply a quantity (such as distance given in inches) by an appropriate unit conversion factor, we convert the quantity to an equivalent value with different units (such as distance in centimeters).

Since $$\mathrm$$, we need to divide the mass in grams by the volume in milliliters.

In general: the number of units of B = the number of units of A $$\times$$ unit conversion factor.

Most measurement units for a given property are directly proportional to one another (y = mx).

Using familiar length units as one example: $\mathrm$ where The Celsius and Fahrenheit temperature scales, however, do not share a common zero point, and so the relationship between these two scales is a linear one rather than a proportional one ($$y = mx b$$).

The necessary conversion factors are given in Table 1.7.1: 1 lb = 453.59 g; 1 L = 1.0567 qt; 1 L = 1,000 m L.

We can convert mass from pounds to grams in one step: $\mathrm\nonumber$ We need to use two steps to convert volume from quarts to milliliters.

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