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 \(K ;\) that is, out of every 100 atoms, 68 are \(\mathrm{K}\) and 32 are \(\mathrm{Na}\). What is the mass percent of potassium in sodium-potassium alloy?

Short answer

The mass percent of potassium in the alloy is approximately 71.2%.

Step-by-step solution

Identify Atomic Masses

First, we need to identify the atomic masses of sodium (Na) and potassium (K). The atomic mass of Na is approximately 23 atomic mass units (amu) and for K it is approximately 39 amu.

Calculate Total Atomic Mass for 100 Atoms

Next, calculate the total atomic mass for 100 atoms in the alloy. Since there are 68 atoms of K and 32 atoms of Na, the total atomic mass is \(68 \times 39 + 32 \times 23\).

Calculate Mass Contribution of Potassium

Calculate the mass contribution of potassium by multiplying the number of K atoms by the atomic mass of K: \(68 \times 39\).

Determine Mass Percent of Potassium

Now, calculate the mass percent of potassium in the alloy using the formula: \(\text{mass percent of K} = \frac{\text{mass of K}}{\text{total mass}} \times 100\).

Plug in Values and Solve

Compute the total mass using the equation from Step 2 to get \(3724\) amu. The mass of K from Step 3 is \(2652\) amu. The mass percent of K is \(\frac{2652}{3724} \times 100 \approx 71.2\).

Key concepts

Atomic Mass

Atomic mass is a fundamental concept that describes the mass of an atom. It is measured in atomic mass units (amu), which is a standard unit used in chemistry to express atomic and molecular weights. To give you an idea, the atomic mass unit is \(1/12\) the mass of a carbon-12 atom.
The atomic mass of an element can be found on the periodic table, and it reflects the weighted average of all the isotopes of that element. For example, in the case of sodium (Na), the atomic mass is around 23 amu, and for potassium (K), it is approximately 39 amu.
Understanding atomic masses is crucial when it comes to calculating the proportions of different atoms in alloys, as seen in the sodium-potassium alloy example, where knowing these values helps in further calculations.

Mass Percent

Mass percent is a way to express the concentration of a component in a mixture. It's calculated by dividing the mass of the component by the total mass of the mixture, then multiplying by 100. This gives a percentage that tells you what portion of the total mass comes from that component.
In our example with the sodium-potassium alloy, the mass percent of potassium was calculated to determine how much of the alloy's mass was due to potassium. By first determining the atomic mass contribution from both sodium and potassium, and then applying the mass percent formula \[ \frac{\text{mass of component}}{\text{total mass}} \times 100 \], we find that the alloy is approximately 71.2% potassium.

Alloys

Alloys are fascinating mixtures of metals or metals combined with non-metals that often exhibit unique properties, different from their individual elements. They are formed to enhance certain characteristics, such as strength, ductility, or resistance to corrosion.
In our situation, the sodium-potassium alloy is noted for being a liquid at relatively low temperatures compared to its constituent metals. This property is beneficial in chemical synthesis, allowing for different reactions to occur more efficiently.
Alloys like Na-K are specified by the atom percent, which in this case is 68 atom percent potassium, meaning out of every 100 atoms in the alloy, 68 are potassium atoms, making the composition more favorable when low melting points are required.

Chemical Synthesis

Chemical synthesis involves the process of creating new compounds or materials from simpler substances through chemical reactions. It is a critical aspect of chemistry, underpinning everything from pharmaceuticals to industrial materials.
The sodium-potassium alloy is used in certain synthesis reactions due to its unique properties, such as being a liquid at room temperature. These reactions may benefit from the alloy's ability to conduct heat and electricity, as well as its favorable reactivity.
Using such alloys allows chemists to devise ways to produce desired products more effectively or to perform reactions that might be challenging under normal circumstances. Hence, the choice of reagents like sodium-potassium alloy can be key in the successful execution of synthetic processes.