Question

One of relatively few reactions that takes place directly between two solids at room temperature is \(\mathrm{Ba}(\mathrm{OH})_{2} \cdot 8 \mathrm{H}_{2} \mathrm{O}(s)+\mathrm{NH}_{4} \mathrm{SCN}(s) \longrightarrow\) \(\mathrm{Ba}(\mathrm{SCN})_{2}(s)+\mathrm{H}_{2} \mathrm{O}(t)+\mathrm{NH}_{3}(g)\) In this equation, the \(\cdot 8 \mathrm{H}_{2} \mathrm{O}\) in \(\mathrm{Ba}(\mathrm{OH})_{2} \cdot 8 \mathrm{H}_{2} \mathrm{O}\) indicates the presence of eight water molecules. This compound is called barium hydroxide octahydrate. a, Balance the equation. b. What mass of ammonium thiocyanate \(\left(\mathrm{NH}_{4} \mathrm{SCN}\right)\) must be used if it is to react completely with \(6.5 \mathrm{~g}\) barium hydroxide octahydrate?

Short answer

The mass of ammonium thiocyanate (NH_4SCN) required to completely react with 6.5 g of barium hydroxide octahydrate (Ba(OH)_2·8H_2O) is approximately 3.135 g.

Step-by-step solution

Balance the chemical equation

The given unbalanced chemical equation is: \( Ba(OH)_2 \cdot 8H_2O(s) + NH_4SCN(s) \rightarrow Ba(SCN)_2(s) + H_2O(l) + NH_3(g) \) To balance the equation, we will adjust the coefficients to make the number of atoms of each element the same on both sides: \( Ba(OH)_2 \cdot 8H_2O(s) + 2NH_4SCN(s) \rightarrow Ba(SCN)_2(s) + 10H_2O(l) + 2NH_3(g) \) Now the chemical equation is balanced.

Find the molar masses of barium hydroxide octahydrate and ammonium thiocyanate

To perform stoichiometric calculations, we require the molar masses of the reactants. We can find these by adding the molar masses of the constituent elements in each compound: \( Molar\ mass\ of\ Ba(OH)_2 \cdot 8H_2O = 137.33 + 2(15.999) + 2(1.007) + 8(2(1.007) + 15.999) \approx 315.51\ g/mol \) \( Molar\ mass\ of\ NH_4SCN = 14.0067 + 4(1.007) + 32.06 + 12.01 + 14.0067 \approx 76.12 g/mol \)

Use the stoichiometry of the balanced equation to find the required mass of ammonium thiocyanate

From the balanced equation, 2 moles of ammonium thiocyanate (NH_4SCN) are required to react with 1 mole of barium hydroxide octahydrate (Ba(OH)_2·8H_2O). Given mass of barium hydroxide octahydrate = 6.5 g First, we calculate the moles of barium hydroxide octahydrate: \( Moles\ of\ Ba(OH)_2 \cdot 8H_2O = \frac{6.5 g}{315.51 g/mol} = 0.0206 mol \) Now, finding the moles of ammonium thiocyanate needed: \( Moles\ of\ NH_4SCN = 2\times Moles\ of\ Ba(OH)_2 \cdot 8H_2O = 2 \times 0.0206 mol = 0.0412 mol \) Finally, finding the mass of ammonium thiocyanate needed: \( Mass\ of\ NH_4SCN = Moles \times Molar\ Mass = 0.0412 mol \times 76.12 g/mol = 3.135 g \)

State the answer

The mass of ammonium thiocyanate (NH_4SCN) required to completely react with 6.5 g of barium hydroxide octahydrate (Ba(OH)_2·8H_2O) is approximately 3.135 g.

Key concepts

Balancing Equations

Balancing chemical equations is an essential skill in chemistry that ensures the law of conservation of mass is satisfied. This law states that matter cannot be created or destroyed in a chemical reaction. To balance an equation, each element must have the same number of atoms on both sides of the equation. Let's take a look at the provided reaction: \( \text{Ba(OH)}_2 \cdot 8\text{H}_2\text{O(s)} + \text{NH}_4\text{SCN(s)} \rightarrow \text{Ba(SCN)}_2\text{(s)} + \text{H}_2\text{O(l)} + \text{NH}_3\text{(g)} \). Initially, count the atoms for each element present. Adjust the coefficients of reactants and products to achieve balance:

• We have 1 molecule of barium hydroxide octahydrate, containing 2 hydroxide ions, and 8 water molecules.
• The balanced form needs 2 molecules of ammonium thiocyanate for consistent atom counts on both sides.
• After balancing, the reaction becomes: \( \text{Ba(OH)}_2 \cdot 8\text{H}_2\text{O(s)} + 2\text{NH}_4\text{SCN(s)} \rightarrow \text{Ba(SCN)}_2\text{(s)} + 10\text{H}_2\text{O(l)} + 2\text{NH}_3\text{(g)} \).

This balanced equation ensures that each element has the same number of atoms on both sides, respecting the law of conservation of mass.

Stoichiometry

Stoichiometry is the quantitative study of reactants and products in chemical reactions. It involves calculations based on the balanced chemical equation to predict the amounts of substances consumed and produced. It's like using a recipe to know how much of each ingredient you need.In the balanced reaction \( \text{Ba(OH)}_2 \cdot 8\text{H}_2\text{O(s)} + 2\text{NH}_4\text{SCN(s)} \rightarrow \text{Ba(SCN)}_2\text{(s)} + 10\text{H}_2\text{O(l)} + 2\text{NH}_3\text{(g)} \), the stoichiometric coefficients indicate the molar relationship between the reactants and products. From this equation:

• 1 mole of barium hydroxide octahydrate reacts with 2 moles of ammonium thiocyanate.
• This provides the basis for mole-to-mole conversion calculations.

For example, if you start with a known mass of barium hydroxide octahydrate, you can use stoichiometry to calculate the necessary mass of ammonium thiocyanate to ensure complete reaction. This is crucial for laboratory preparation and industrial applications, where precise measurements are key.

Molar Mass

Molar mass is a foundational concept in chemistry denoting the mass of one mole (6.022 x 10²³ particles) of a substance. It is typically expressed in grams per mole (g/mol) and is calculated by summing the atomic masses of all atoms in the chemical formula. Here’s how we calculate it for the compounds in this reaction:- **Barium Hydroxide Octahydrate (Ba(OH)₂·8H₂O):** - Barium: \(137.33\) g/mol - Oxygen in hydroxide: \(2 \times 15.999\) g/mol - Hydrogen in hydroxide: \(2 \times 1.007\) g/mol - Water: \(8 \times (2 \times 1.007 + 15.999)\) g/mol - Totaling approximately to \(315.51 g/mol\)- **Ammonium Thiocyanate (NH₄SCN):** - Nitrogen: \(14.0067\) g/mol - Hydrogen: \(4 \times 1.007\) g/mol - Sulfur: \(32.06\) g/mol - Carbon: \(12.01\) g/mol - Another Nitrogen: \(14.0067\) g/mol - Totaling approximately to \(76.12 g/mol\)Understanding molar mass allows us to convert from mass to moles and vice versa, facilitating the stoichiometric calculations required for balancing chemical reactions and determining reactant and product quantities.

Solid-state Chemistry

Solid-state chemistry focuses on the study of solid materials, their synthesis, structure, and properties. It examines reactions that occur in the solid-state environment, often exhibiting remarkable differences compared to those occurring in liquid or gaseous states. For instance, the reaction \( \text{Ba(OH)}_2 \cdot 8\text{H}_2\text{O(s)} + \text{NH}_4\text{SCN(s)} \rightarrow \text{Ba(SCN)}_2\text{(s)} + \text{H}_2\text{O(l)} + \text{NH}_3\text{(g)} \) is unique because it involves reactants that are initially solid.Solid-state reactions are typically slower. However, the reaction here is fascinating due to its direct room temperature synthesis, which is uncommon. In this process:

• The solids interact at the atomic level, allowing the rearrangement of atoms to form new products.
• The reaction is driven by the release of ammonia gas, which acts as a driving force in the transformation.

Understanding solid-state reactions is vital for applications such as material synthesis, nanotechnology, and the creation of electronic components, offering insights into how materials behave, combine, and can be manipulated.