A mixture of \(1.00 \mathrm{~g} \mathrm{H}_{2}\) and \(1.00 \mathrm{~g} \mathrm{He}\) is placed in a \(1.00-\mathrm{L}\) container at \(27^{\circ} \mathrm{C}\). Calculate the partial pressure of each gas and the total pressure.

The Ideal Gas Law is a fundamental principle in chemistry that relates the pressure, volume, temperature, and the number of moles of an ideal gas. It is represented by the equation \(PV=nRT\), where \(P\) stands for pressure, \(V\) represents volume, \(n\) is the number of moles, \(R\) is the gas constant, and \(T\) is the temperature in Kelvin.

The gas constant \(R\) has different values depending on the units used, but for the purpose of calculating pressure in atmospheres (atm) when volume is in liters (L), moles (mol), and temperature in Kelvin (K), the value is typically \(0.0821 L\cdot atm/mol\cdot K\). Temperature must always be in Kelvin for the Ideal Gas Law to be accurate, as the Kelvin scale is an absolute scale with \(0\) being absolute zero.

This law is especially useful because it allows us to solve for any single variable if we know the other three. For example, in the exercise, we use the Ideal Gas Law to find out the partial pressure exerted by each gas in a mixture by rearranging the formula to \(P = \frac{nRT}{V}\).

Molar mass conversion is essential when working with gases to convert between mass and moles, as calculations involving gases often use moles rather than grams. The molar mass is defined as the mass of one mole of a substance, and it is usually expressed in grams per mole (g/mol).

For instance, in the given problem, the molar mass of hydrogen (H2) is \(2\ g/mol\), while that of helium (He) is \(4\ g/mol\). To find the number of moles (\(n\)) from the given mass, you divide the mass of the gas by its molar mass (\(n = \frac{mass}{molar\_mass}\)). This step is crucial because the Ideal Gas Law requires the amount of gas to be in moles.

Once the number of moles is determined, as shown in the exercise, one can proceed to use the Ideal Gas Law and other related calculations. Remember that precise molar mass values are necessary for accurate results.

When dealing with a mixture of gases, like the one described in the exercise, the total pressure can be perceived as the sum of the partial pressures of each individual gas in the mixture. This concept is described by Dalton's Law of Partial Pressures.

Dalton's Law states that for a mixture of non-reacting gases, the total pressure exerted by the mixture is equal to the sum of the partial pressures of individual gases. Each gas in the mixture exerts pressure as if it were the only gas present, and can be calculated using the Ideal Gas Law.

In our example, after finding the partial pressures of hydrogen (H2) and helium (He) separately, we simply add them to find the total pressure of the gas mixture (\(P_{total} = P_{H2} + P_{He}\)). Knowing how to calculate the partial pressures and the total pressure of a mixture is vital in understanding how gases behave in different environments and is also used in various scientific and industrial applications.