Question

One of relatively few reactions that takes place directly between two solids at room temperature is $$ \mathrm{Ba}(\mathrm{OH})_{2} \cdot 8 \mathrm{H}_{2} \mathrm{O}(s)+\mathrm{NH}_{4} \mathrm{SCN}(s) \longrightarrow $$ 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 pres- ence 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 balanced chemical equation is \(Ba(OH)_2 \cdot 8 H_2O(s) + 2NH_4SCN(s) \rightarrow Ba(SCN)_2(s) + 9H_2O(l) + 2NH_3(g)\). To react completely with 6.5 g of barium hydroxide octahydrate (Ba(OH)2 · 8H2O), 3.14 g of ammonium thiocyanate (NH4SCN) must be used.

Step-by-step solution

Balance the chemical equation

First, we need to identify the products of the reaction. The given reactants are barium hydroxide octahydrate (Ba(OH)2 · 8H2O) and ammonium thiocyanate (NH4SCN). The products of this reaction are barium thiocyanate (Ba(SCN)2) and water (H2O) and ammonia (NH3). Unbalanced equation: \(Ba(OH)_2 \cdot 8 H_2O(s) + NH_4SCN(s) \rightarrow Ba(SCN)_2(s) + H_2O(l) + NH_3(g) \) Now, balance the elements in the equation one by one: 1. There are 2 SCN in the product side, so we need 2 moles of NH4SCN on the reactant side. Update the equation: \(Ba(OH)_2 \cdot 8 H_2O(s) + 2NH_4SCN(s) \rightarrow Ba(SCN)_2(s) + H_2O(l) + NH_3(g) \) 2. Now, balance the hydrogen and oxygen atoms. There are (2+16) 18 hydrogen atoms and 8 oxygen atoms on the reactant side. On the product side, we require 1 mole of water and 2 moles of ammonia to balance these atoms. Update the equation: \(Ba(OH)_2 \cdot 8 H_2O(s) + 2NH_4SCN(s) \rightarrow Ba(SCN)_2(s) + 9H_2O(l) + 2NH_3(g) \) Now the chemical equation is balanced.

Calculate the mass of ammonium thiocyanate required

To calculate the mass of ammonium thiocyanate (NH4SCN) required, we can use stoichiometry. The balanced chemical equation gives us the mole ratio of reactants and products. From the balanced equation: \(1 \: mole \: Ba(OH)_2 \cdot 8H_2O \: \rightarrow \: 2 \: moles \: NH_4SCN\) First, we need to calculate the number of moles of barium hydroxide octahydrate (Ba(OH)2 · 8H2O) in 6.5 g. Molar mass of Ba(OH)2 · 8H2O: \(137.3 (Ba) + 2 \times 15.999 (O) + 2 \times 1.008 (H) + 8 \times (2 \times 1.008 (H) + 15.999 (O)) \\ = 137.3 + 31.998 + 16.032 + 8 \times 18.015 \\ = 315.51 \: g/mol\) Moles of Ba(OH)2 · 8H2O = \(\frac{6.5}{315.51} = 0.0206 \: moles\) Using stoichiometry, we can find the moles of ammonium thiocyanate (NH4SCN) required: Moles of NH4SCN = \(0.0206 \times 2 = 0.0412 \: moles\) Now, calculate the mass of 0.0412 moles of NH4SCN: Molar mass of NH4SCN: \(14.007 (N) + 4 \times 1.008 (H) + 32.065 (S) + 12.011 (C) + 14.007 (N) \\ = 14.007 + 4.032 + 32.065 + 12.011 + 14.007 \\ = 76.122 \: g/mol\) Mass of NH4SCN = \(0.0412 \times 76.122 = 3.14 \: g\) Thus, 3.14 g of ammonium thiocyanate (NH4SCN) must be used to react completely with 6.5 g of barium hydroxide octahydrate (Ba(OH)2 · 8H2O).

Key concepts

Chemical Reaction Balancing

Chemical reactions must be balanced to comply with the law of conservation of mass, which states that matter cannot be created or destroyed in a closed system. During the balancing process, the number of atoms for each element on the reactant side (left side of the equation) must equal the number on the product side (right side of the equation).
For example, in the reaction between barium hydroxide octahydrate (\(\mathrm{Ba(OH)_2 \cdot 8H_2O}\)) and ammonium thiocyanate (\(\mathrm{NH_4SCN}\)), the initial unbalanced equation might leave more atoms of an element on one side. Hence, we use coefficients to multiply the compounds such that both sides reflect an equal number.

• Start by balancing complex molecules or polyatomic ions first, if possible.
• Balance metals, non-metals, and hydrogen and oxygen atoms consecutively.
• After updating the equation, verify that the atom count for each element is equivalent on both sides.

Thus, the balanced equation represents the exact relationship of the reactants and products in a chemical reaction, preserving atomic balance and ensuring a clear understanding of the chemical process.

Molar Mass Calculation

Understanding molar mass plays a vital role in stoichiometry, allowing us to convert between grams and moles — a fundamental aspect of chemical calculations. Molar mass is essentially the mass of one mole of a substance (expressed in g/mol) and can be calculated by summing the atomic weights of all atoms present in a compound.
For instance, the molar mass of barium hydroxide octahydrate (\(\mathrm{Ba(OH)_2 \cdot 8H_2O}\)) involves adding the atomic masses of barium, oxygen, hydrogen, and the water of hydration. Calculate it like so:

• Atomic mass of Ba: 137.3
• 2 O: 2 \times 15.999
• 2 H: 2 \times 1.008
• 8 molecules of water, \(8 \times (2 \times 1.008 + 15.999)\)

The total gives us 315.51 g/mol for \(\mathrm{Ba(OH)_2 \cdot 8H_2O}\). Similarly, the molar mass of ammonium thiocyanate (\(\mathrm{NH_4SCN}\)) is determined using its atomic composition: nitrogen (N), hydrogen (H), sulfur (S), and carbon (C). This calculation ensures you can accurately find the moles from a given mass, a step necessary for the stoichiometric balance used in chemical equations.

Solid State Reactions

Solid state reactions, like the one described in the original exercise, are chemical reactions that occur between solid compounds. These reactions are less common under standard conditions, but they provide useful insights in material science and chemistry.
Unlike reactions in solutions, solid state reactions often have slower kinetics due to limited diffusion of reactants through the solid matrices. They typically require a higher activation energy and can sometimes be enhanced through heating, which increases the vibrational energy of the solid lattice, thereby facilitating the reaction.
Key aspects of solid state reactions include:

• Reactant phases: Both reactants remain solids through the process, and diffusion is the primary mechanism for atom exchange.
• Applications: Often used in the production of ceramics and other material syntheses where liquid solutions would be undesirable.
• Conditions: While some reactions might occur at room temperature (like in the exercise), many require elevated temperatures to proceed at noticeable rates.

Understanding these reactions gives learners a window into the multitude of ways materials can be manipulated and synthesized beyond conventional liquid-phase chemistry.