Question

Consider the following reaction: $$ \mathrm{Ca}(s)+\mathrm{Cl}_{2}(g) \rightarrow \mathrm{CaCl}_{2}(s) $$ What volume of chlorine gas at \(25^{\circ} \mathrm{C},\) and \(1.02 \mathrm{atm}\) would be necessary to react completely with \(4.15 \mathrm{g}\) of calcium metal?

Short answer

The volume of chlorine gas required to react completely with 4.15 grams of calcium metal is approximately 2.49 liters at \(25^{\circ}C\) and 1.02 atm.

Step-by-step solution

Calculate the moles of calcium

First, we need to determine the number of moles of calcium (\(Ca\)). We can do this using its molar mass given as: Molar mass of \(Ca = 40.08 \, g/mol\) Now, we can calculate the moles of calcium metal using the given mass and molar mass of calcium: \[ n_{Ca} = \frac{mass_{Ca}}{Molar \, mass_{Ca}} = \frac{4.15 \, g}{40.08 \, g/mol} = 0.1035 \, mol \]

Determine the stoichiometry of the reaction

From the given balanced chemical equation, we see that: \[\ 1 \, mol \, of \, Ca \, reacts \, with \, 1 \, mol \, of \, Cl_{2} \] So, \(1 \, mol \, of \, Cl_{2}\) is needed for \(1 \, mol \, of \, Ca\). Thus, \(0.1035 \, mol \, of \, Cl_{2}\) is needed for \(0.1035 \, mol \, of \, Ca\).

Calculate the volume of chlorine gas using the Ideal Gas Law

Now that we know the moles of chlorine gas required, we can use the Ideal Gas Law to determine the volume. The Ideal Gas Law is: \[ PV = nRT \] Where \(P\) is pressure (in atm), \(V\) is volume (in L), \(n\) is the number of moles, \(R\) is the ideal gas constant \(0.0821 \, L \cdot atm/mol \cdot K\), and \(T\) is the temperature in Kelvin (K). First, convert temperature from Celsius to Kelvin: \(T = 25^{\circ}C + 273.15 = 298.15 \, K\) Now, we can rearrange the Ideal Gas Law to find the volume \(V\): \[ V = \frac{nRT}{P} \] Finally, plug in the known values and solve for the volume of chlorine gas: \[ V = \frac{(0.1035 \, mol)(0.0821 \, L \cdot atm/mol \cdot K)(298.15 \, K)}{1.02 \, atm} = 2.49 \, L \] The volume of chlorine gas required to react completely with 4.15 grams of calcium metal is approximately 2.49 liters at \(25^{\circ}C\) and 1.02 atm.

Key concepts

Stoichiometry

Stoichiometry is all about measuring the amounts of reactants and products in a chemical reaction. It is like a recipe in cooking but for chemistry! In the given reaction of calcium with chlorine gas to form calcium chloride, stoichiometry helps us know how much of one reactant is needed to completely react with another.
Understanding stoichiometry requires balancing chemical equations and using mole ratios. Mole ratios come from the coefficients in a balanced chemical equation. For example, in the reaction \( \mathrm{Ca}(s) + \mathrm{Cl}_{2}(g) \rightarrow \mathrm{CaCl}_{2}(s) \), one mole of calcium reacts with one mole of chlorine gas. Therefore, if you start with 0.1035 moles of calcium, you need the same amount, 0.1035 moles, of chlorine.
But why do balanced equations matter? They ensure that you have the same number of each type of atom on both sides of the equation. That means mass is conserved, just like counting ingredients in a recipe.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products through the breaking and forming of bonds.
In our example, calcium reacts with chlorine gas to produce calcium chloride. This reaction is a synthesis reaction, where two or more reactants combine to form a single product. Synthesis reactions are just one of many types of chemical reactions. Others include decomposition, single replacement, and combustion reactions.
Reactants and products are the core players in any chemical reaction. Reactants are the starting substances that undergo changes, while products are the new substances formed. So, here calcium (Ca) and chlorine gas (Cl\(_2\)) are the reactants, and calcium chloride (CaCl\(_2\)) is the product.

• Understanding the nature of the chemical reaction lets us anticipate and calculate the products formed and reactants consumed.

Molar Mass

Molar mass is a central concept in chemistry for converting between grams and moles, which are the units chemists often use to measure quantities of substances.
The molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For example, the molar mass of calcium is 40.08 g/mol, meaning every 1 mole of calcium weighs 40.08 grams. This is essential to know when you want to convert the mass of a substance into the number of moles. Remember, moles help us count particles at the atomic level!
In our exercise, you use the relationship \(\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}\) to convert mass into moles.
This conversion allowed us to determine the number of moles of calcium we started with in the reaction, which in turn helped us use stoichiometry to find out the moles, and thus the volume, of chlorine gas required.