Solving Real Problems With Chemistry Assigning Quantum Numbers
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.
This is why it is referred to as the factor-label method.
As your study of chemistry continues, you will encounter many opportunities to apply this approach.
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\[x\:\mathrm\nonumber\] We write the unit conversion factor in its two forms: \[\mathrm\nonumber\] The correct unit conversion factor is the ratio that cancels the units of grams and leaves ounces.
\[\begin x\:\ce&=\mathrm\ &=\mathrm\ &=\mathrm \end\] (units) will appropriately cancel and/or combine to yield the desired unit in the result.
Now, consider using this same relation to predict the time required for a person running at this speed to travel a distance of 25 m.
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 mercury or alcohol in a common glass thermometer changes its volume as the temperature changes.
Because the volume of the liquid changes more than the volume of the glass, we can see the liquid expand when it gets warmer and contract when it gets cooler.