\(23 \mathrm{~g}\) sodium metal reacts with water. Calculate the : (a) volume of \(\mathrm{H}_{2}\) liberated at NTP, (b) moles of \(\mathrm{H}_{2}\) liberated, (c) weight of \(\mathrm{H}_{2}\) liberated.

Understanding how to balance a chemical equation is crucial for solving stoichiometry problems. Chemical reactions follow the law of conservation of mass which states that matter is neither created nor destroyed. Balancing a chemical equation ensures that the number of atoms of each element is the same on both sides of the equation.

For instance, the reaction between sodium metal and water is represented by the equation:
\[2\mathrm{Na} + 2\mathrm{H}_2\mathrm{O} \rightarrow 2\mathrm{NaOH} + \mathrm{H}_2\].
We start by counting the atoms of each element in the reactants and products. The equation balances when there are equal numbers of sodium, hydrogen, and oxygen atoms before and after the reaction.
Balancing equations allows us to determine the stoichiometry of the reaction - the ratio in which compounds react and are produced. In this example, two moles of sodium react with two moles of water to produce two moles of sodium hydroxide and one mole of hydrogen gas, demonstrating a 2:1 reaction ratio for sodium to hydrogen gas.

The mole concept is a fundamental principle in chemistry that links the mass of a substance to its number of particles, such as atoms or molecules. One mole is defined as exactly 6.022 x 10²³ particles, which is Avogadro's number.

Understanding the mole concept allows chemists to count particles by weighing, as demonstrated in our exercise:
\[\text{Moles of sodium} = \frac{23 g}{22.99 g/mol} = 1 mol\].
Here, we convert the mass of sodium used in the reaction to moles by dividing by its molar mass (22.99 g/mol). This calculation indicates that there is 1 mole of sodium, or approximately 6.022 x 10²³ sodium atoms, participating in the reaction.
Applying the mole concept to stoichiometry problems is essential because it facilitates the use of balanced chemical equations to predict the amounts of reactants and products involved in a chemical reaction.

Gas laws help us understand and predict the behavior of gases under different conditions of temperature and pressure. At Normal Temperature and Pressure (NTP), which is 0°C and 1 atmosphere, one mole of any ideal gas occupies 22.4 liters.

This principle is used in our exercise to determine the volume of hydrogen gas produced:
\[\text{Volume of }\mathrm{H}_2 = 0.5 \text{ moles} \times 22.4 \text{ liters/mole} = 11.2 \text{ liters}\].
The relationship between the amount of gas (in moles) and its volume at NTP allows us to use the stoichiometry of the reaction to find out how much gas is produced. If we were working under conditions other than NTP, we would use the Ideal Gas Law, \(PV=nRT\), to relate pressure (P), volume (V), temperature (T), and the number of moles (n) of the gas, with R being the gas constant.
In summary, gas laws are vital for predicting the volume that gas will occupy, which is particularly important in reactions that produce gases, as seen with the liberation of hydrogen gas in the reaction between sodium and water.