Question

The weight of a single atom of oxygen is (a) \(5.057 \times 10^{23} \mathrm{~g}\) (b) \(1.556 \times 10^{23} \mathrm{~g}\) (c) \(2.656 \times 10^{-23} \mathrm{~g}\) (d) \(4.538 \times 10^{-23} \mathrm{~g}\)

Short answer

(c) \(2.656 \times 10^{-23} \mathrm{~g}\)

Step-by-step solution

Identify the Atomic Mass of Oxygen

The atomic mass of oxygen is approximately 16 atomic mass units (amu). We will need this value to calculate the weight of a single oxygen atom.

Convert Atomic Mass to Grams

Atomic mass units are converted to grams using the conversion factor where 1 amu = \(1.66 \times 10^{-24} \mathrm{~g}\). Multiply the atomic mass of oxygen (16 amu) by this conversion factor:\[16 \times 1.66 \times 10^{-24} = 2.656 \times 10^{-23} \mathrm{~g}\]

Compare Given Options to Calculated Value

Review the options given in the exercise and find the one that matches the calculated weight:- (a) \(5.057 \times 10^{23} \mathrm{~g}\)- (b) \(1.556 \times 10^{23} \mathrm{~g}\)- (c) \(2.656 \times 10^{-23} \mathrm{~g}\)- (d) \(4.538 \times 10^{-23} \mathrm{~g}\)The option that matches our calculation is (c) \(2.656 \times 10^{-23} \mathrm{~g}\).

Key concepts

Understanding Atomic Mass Unit (amu)

Atoms are incredibly tiny, and their weight is measured using a special unit called the atomic mass unit, or amu for short. It's a standard way scientists express atomic and molecular weights. One atomic mass unit is defined as a twelfth of the mass of a carbon-12 atom. The carbon-12 atom stands as a universal reference point.

Why use amu instead of grams? Simply put, the numbers become more manageable. It's much easier to say an oxygen atom has a mass of 16 amu instead of trying to wrap our heads around an infinitesimally small value in grams. Remembering that the atomic mass of oxygen is about 16 amu is essential when calculating the mass of a single oxygen atom.

Applying Conversion Factors

When determining the weight of an atom in grams, we need to convert from atomic mass units to real-world grams using a conversion factor. A conversion factor is a ratio that allows us to switch between two different units of measurement without changing the value.

In this case, the conversion factor is: 1 amu = \(1.66 \times 10^{-24}\) grams. This tiny number reflects just how small atoms are compared to everyday objects. To convert the atomic mass of oxygen (16 amu) to grams, you multiply by this conversion factor:

• 16 amu \(\times 1.66 \times 10^{-24} = 2.656 \times 10^{-23}\) grams

Understanding and applying conversion factors correctly is crucial in translating between units, whether you're working in chemistry, physics, or everyday tasks like cooking!

Oxygen Atom Calculation Explained

Now that we've broken down the units, let's focus on calculating the weight of a single oxygen atom. We determined earlier that the weight is 16 amu. When converted to grams, using the conversion factor, we found it to be \(2.656 \times 10^{-23}\) grams.

How did we get here? We multiplied the atomic mass of oxygen (16) by the conversion factor (\(1.66 \times 10^{-24}\) grams/amu). This calculation ensures that we get accurate results for the weight of a single atom.

Once we calculated the oxygen atom's weight, we compared it with the options given:

• (a) \(5.057 \times 10^{23} \mathrm{~g}\)
• (b) \(1.556 \times 10^{23} \mathrm{~g}\)
• (c) \(2.656 \times 10^{-23} \mathrm{~g}\)
• (d) \(4.538 \times 10^{-23} \mathrm{~g}\)

Only option (c) matches the calculated value. This step-by-step process demonstrates how using atomic mass units and conversion factors can simplify complex calculations.