Problem 67 - Chemistry and Chemical Reactivity

Question

A reagent occasionally used in chemical synthesis is sodium-potassium alloy. (Alloys are mixtures of metals, and Na-K has the interesting property that it is a liquid.) One formulation of the alloy (the one that melts at the lowest temperature) contains 68 atom percent \(\mathbf{K} ;\) that is, out of every 100 atoms, 68 are \(\mathrm{K}\) and 32 are \(\mathrm{Na}\). What is the weight percent of potassium in sodium-potassium alloy?

Step-by-Step Solution

Answer

The weight percent of potassium is 78.31%.

Step 1: Calculate Atomic Weights

First, note the standard atomic weights of potassium (\( K \)) and sodium (\( Na \)), which are approximately \( 39.10 \) g/mol and \( 22.99 \) g/mol, respectively.

Step 2: Determine Moles of Atoms in a Sample

In a sample with 100 total atoms, we have: \( 68 \) atoms of \( K \) and \( 32 \) atoms of \( Na \).

Step 3: Calculate Mass of Potassium

The mass of \( 68 \) atoms of \( K \) is given by: \[ 68 \text{ atoms} \times 39.10 \text{ g/mol} = 2656.80 \] atomic mass units (amu).

Step 4: Calculate Mass of Sodium

The mass of \( 32 \) atoms of \( Na \) is given by: \[ 32 \text{ atoms} \times 22.99 \text{ g/mol} = 735.68 \] amu.

Step 5: Calculate Total Mass of Alloy Sample

The total mass of the 100-atom sample is: \[ 2656.80 \text{ amu} + 735.68 \text{ amu} = 3392.48 \text{ amu} \]

Step 6: Calculate Weight Percent of Potassium

The weight percent of \( K \) in the alloy is calculated as: \[ \text{Weight percent of } K = \left( \frac{2656.80}{3392.48} \right) \times 100 \% = 78.31 \% \]

Key Concepts

Atomic Weights

When dealing with elements like sodium (Na) and potassium (K), understanding atomic weights is crucial. Atomic weight refers to the average mass of atoms of an element, typically expressed in atomic mass units (amu).
It is essential to note that atomic weights take into account the weighted average of all isotopes of an element, distributed naturally. For potassium and sodium, these values are approximately 39.10 g/mol and 22.99 g/mol, respectively.
These atomic weights help in calculating the mass of elements when they participate in chemical reactions or combine to form compounds, like alloys.

• Potassium (K) – 39.10 g/mol
• Sodium (Na) – 22.99 g/mol

Knowing the atomic weights allows chemists to determine how elements will combine and in what proportions.

Weight Percent Calculation

Weight percent is a way of expressing concentration of an element in a compound or mixture. It tells us how much of an element contributes to the total weight of a substance. To calculate it, you divide the total mass of the specific element by the total mass of the compound and then multiply by 100.
For the sodium-potassium alloy, this means dividing the mass of potassium by the total mass of the alloy and converting it into a percentage.
Let's say, in a given sample of the alloy, we have the following:

• Mass of potassium: 2656.80 amu
• Total mass of the sample: 3392.48 amu

The weight percent of potassium would be computed as:

• \[\text{Weight percent of } K = \left( \frac{2656.80}{3392.48} \right) \times 100 \% = 78.31 \%\]

Understanding this calculation helps to grasp how much each element contributes to the overall composition of an alloy or mixture.

Chemical Synthesis

Chemical synthesis involves constructing complex chemical compounds from simpler ones. This process may employ reagents like sodium-potassium alloy due to their unique properties. The synthesis process can vary widely but generally includes strategic combination of elements and compounds to produce a desired chemical product.
Sodium-potassium alloy is occasionally used in these syntheses because of its unusual property – being liquid at room temperature. This liquid form can facilitate different types of reactions, especially in organic and inorganic chemistry. This can lead to the creation of new compounds or modification of existing ones.

• Involves combining chemical elements.
• Sodium-potassium alloy acts as a reactive agent.
• Facilitates transformations by modifying conditions or reacting directly.

The use of sodium-potassium alloys in chemical synthesis showcases the versatile nature of alloys beyond their metallic characteristics.

Alloy Composition

Alloy composition refers to the proportion of elements mixed together to form an alloy. Alloys like sodium-potassium are mixtures that display unique characteristics, different from those of the individual metals that make them up.
The composition can greatly influence the properties of the alloy, such as its melting point, density, and reactivity. In the case of sodium-potassium alloy, the specific composition of 68 atoms of potassium and 32 atoms of sodium creates an alloy that is liquid at room temperature.
This specific blend in composition is crucial as it provides the alloy with its unique qualities:

• Melting point adjustment – critical for certain applications.
• Enhanced reactivity as a liquid.
• Potential to act as a medium in chemical reactions.

Understanding alloy composition, therefore, helps in designing materials with tailored properties for specific applications in science and industry.