Sistemas y Conversión de Unidades - Guía de Química General

Session Overview and Administrative Context

The General Chemistry Guide for the Propaedeutic Course at the Faculty of Chemistry, specifically for the 2026-2 period, outlines the essential foundational skills required for the course. The IX Review Session, dated October 19, marks a critical point in the academic timeline. Important upcoming exam dates are noted for October 17 and October 24. A significant portion of this session focuses on concentration, including mass percentage, volume percentage of a solution, and molarity.

Systems and Unit Conversion Fundamentals

Unit conversion is defined as the process of transforming a specific quantity expressed in a particular unit of measurement into an equivalent value in a different unit. This transformation can occur between units of the same system or between different systems of measurement entirely. To achieve this, mathematical operations known as conversion factors are utilized. These factors facilitate the establishment of equivalencies between the multiples and submultiples of a given unit of measurement.

Conversion factors are structurally expressed as fractions. In these fractions, the numerator and the denominator represent identical quantities, although they are expressed using different units of measure. This mathematical property allows for the multiplication of a value by a factor of 1 without changing the physical magnitude, only the representation of that magnitude in terms of units.

Procedural Steps for Unit Conversion

To convert a specific quantity from one unit to another, a systematic set of steps must be followed. Using the example of converting $2.0\,\text{horas}$ to minutes, the process begins by identifying the unit that needs to be eliminated and placing it in the denominator of the conversion factor. Conversely, the unit to which the quantity is being converted is placed in the numerator. For this specific scenario, since $1.0\,\text{hora}$ is equal to $60.0\,\text{minutos}$, the factor is written accordingly.

Once the factor is established, the original value is multiplied by the numerator. In the case of $2.0\,\text{horas}$, the calculation follows as $2.0\,\text{horas} \times \frac{60.0\,\text{minutos}}{1.0\,\text{hora}} = 120.0\,\text{minutos}$. It is important to observe that the units being eliminated are those located transversally to each other; in this instance, hours in the original value cancel out the hours in the denominator of the conversion factor, leaving only minutes in the final result.

Conversion of Composite Units

In instances where composite units are present, such as velocity expressed in meters per second ($\text{m/s}$) or similar units involving multiple dimensions, the procedure involves a specific adjustment for the unit located in the denominator. For the denominator unit, the process is reversed: one multiplies by the unit to be eliminated and divides by the required unit. This often necessitates the use of multiple conversion factors simultaneously.

An example of this procedure is the conversion of $120.0\,\text{km/h}$ to $\text{m/s}$. This requires two distinct conversion factors: one to transform kilometers to meters and another to transform hours to seconds. The first factor relies on the equivalence $1.0\,\text{km} = 1000.0\,\text{m}$, and the second factor relies on the equivalence $1.0\,\text{hora} = 3600.0\,\text{s}$. The combined operation is expressed as $120.0\,\frac{\text{km}}{\text{h}} \times \frac{1000.0\,\text{m}}{1.0\,\text{km}} \times \frac{1.0\,\text{hora}}{3600.0\,\text{s}} = 33.3\,\text{m/s}$.

International System of Units (SI) Base Units

The International System of Units identifies seven fundamental physical magnitudes, each with a specific basic unit and symbol. Length is measured in the meter ($\text{m}$). Time is measured in the second ($\text{s}$). Mass is measured in the kilogram ($\text{kg}$). The intensity of electric current is measured in the ampere ($\text{A}$). Temperature is measured in the Kelvin ($\text{K}$). The amount of substance is measured in the mol ($\text{mol}$). Luminous intensity is measured in the candela ($\text{cd}$).

Prefixes for Multiples and Submultiples

Prefixes are used to indicate powers of ten associated with a base unit, facilitating the expression of very large or very small quantities. Multiples include Deca ($\text{da}$) for $10^{1}$, Hecto ($\text{h}$) for $10^{2}$, Kilo ($\text{k}$) for $10^{3}$, Mega ($\text{M}$) for $10^{6}$, Giga ($\text{G}$) for $10^{9}$, Tera ($\text{T}$) for $10^{12}$, Peta ($\text{P}$) for $10^{15}$, and Exa ($\text{E}$) for $10^{18}$.

Submultiples indicate fractional parts of a unit and include Deci ($\text{d}$) for $10^{-1}$, Centi ($\text{c}$) for $10^{-2}$, Mili ($\text{m}$) for $10^{-3}$, Micro ($\mu$) for $10^{-6}$, Nano ($\text{n}$) for $10^{-9}$, Pico ($\text{p}$) for $10^{-12}$, Femto ($\text{f}$) for $10^{-15}$, and Atto ($\text{a}$) for $10^{-18}$.

Equations and Physical Equivalencies

For the magnitude of length, common equivalencies include $1.0\,\text{pie} = 30.48\,\text{cm}$, $1.0\,\text{yarda} = 91.44\,\text{cm}$, $1.0\,\text{pulgada} = 2.54\,\text{cm}$, $1.0\,\text{milla} = 1760.0\,\text{yardas}$, and $1.0\,\text{ángstrom (Å)} = 1.0 \times 10^{-10}\,\text{m}$. In terms of mass ($m$), the equivalencies are defined as $1.0\,\text{libra} = 0.454\,\text{kg}$ and $1.0\,\text{libra} = 16.0\,\text{oz}$. For volume ($V$), the standard conversions are $1.0\,\text{L} = 1000.0\,\text{cm}^3$ and $1.0\,\text{galón} = 3.78\,\text{L}$. Pressure ($p$) is often converted using the relation $1.0\,\text{atm} = 760.0\,\text{mmHg}$.

Temperature conversions utilize specific formulas to transition between Celsius (${}^\circ\text{C}$), Fahrenheit (${}^\circ\text{F}$), Kelvin ($\text{K}$), and Rankine ($\text{R}$). To find Fahrenheit, the formula is ${}^\circ\text{F} = \frac{9}{5} {}^\circ\text{C} + 32$. To find Celsius from Fahrenheit, the formula is ${}^\circ\text{C} = \frac{5}{9} ({}^\circ\text{F} - 32)$. Absolute temperature in Kelvin is calculated as $K = 273.15 + {}^\circ\text{C}$, while Rankine is calculated as $R = {}^\circ\text{F} + 459.67$.

Gas dynamic equations and other physical properties are defined by various laws. Boyle's Law is expressed as $p_1 V_1 = p_2 V_2$. Charles's Law is expressed as $\frac{V_1}{T_1} = \frac{V_2}{T_2}$. The combined gas law is written as $\frac{p_1 V_1}{T_1} = \frac{p_2 V_2}{T_2}$. The Ideal Gas Law is $PV = nRT$, where the universal gas constant $R$ is defined as $0.082\,\text{atm L mol}^{-1}\,\text{K}^{-1}$. Density ($\rho$) is defined by the ratio of mass to volume, expressed as $\rho = \frac{m}{V}$.

Practice Exercises

The curriculum includes practical problems to apply these conversion principles. The first exercise requires calculating the capacity in liters of a box that measures $0.6\,\text{m}$ in length, $20.0\,\text{cm}$ in width, and $50.0\,\text{mm}$ in depth. The second exercise asks for the calculation of the total number of seconds contained within a single day.