Problem 163 - Introductory Chemistry Atoms First

Question

Indicate whether or not the following volumes are quantized: (a) The volume of water available in \(16-\mathrm{oz}\) bottles (b) The volume of water available from a drinking fountain (c) The volume of soft drink available from a soda-fountain dispenser (d) The volume of soft drink available in \(12-\mathrm{oz}\) cans

Step-by-Step Solution

Answer

(a) The volume of water available in 16-oz bottles is quantized since it can only be present in multiples of 16 ounces. (b) The volume of water available from a drinking fountain is not quantized since it can be any arbitrary value. (c) The volume of soft drink available from a soda-fountain dispenser is not quantized, as it can also be any arbitrary value. (d) The volume of soft drink available in 12-oz cans is quantized, as it can only be multiples of 12 ounces.

Step 1: (a) Analyzing the volume of water in 16-oz bottles

The volume of water available in 16-oz bottles is in fixed, discrete amounts. Each bottle contains 16 ounces of water, so the volume can only be present in multiples of 16 ounces (e.g., 16, 32, 48 ounces, etc.). Therefore, the volume is quantized.

Step 2: (b) Analyzing the volume of water from a drinking fountain

The volume of water available from a drinking fountain is not fixed to specific amounts. People can collect water in various amounts by controlling the time the fountain is activated. Thus, the volume of water from a drinking fountain can be any arbitrary value, making the volume not quantized.

Step 3: (c) Analyzing the volume of soft drink from a soda-fountain dispenser

Similarly to the drinking fountain, the volume of soft drink available from a soda-fountain dispenser can also be any arbitrary value. People can control the amount of soft drink they get by controlling the time the dispenser is activated, which leads to variable, non-discrete amounts. Thus, the volume is not quantized.

Step 4: (d) Analyzing the volume of soft drink in 12-oz cans

Just like the 16-oz water bottles, the volume of soft drink in 12-oz cans is also quantized. Each can contains 12 ounces of soft drink, so the volume can only be presented in multiples of 12 ounces (e.g., 12, 24, 36 ounces, etc.). Consequently, the volume is quantized.

Key Concepts

Discrete Volume

In the context of measuring physical quantities like liquid, discrete volume refers to quantities that are available in fixed or set amounts. Imagine purchasing water in 16-ounce bottles. Here, each bottle represents a specific, unchangeable measure of volume. You can't take a portion of the bottle — it's either the full 16 ounces or nothing.

Discrete volume is quantized, meaning it comes in individual, distinct units or packets.

• 16 oz water bottles
• 12 oz soda cans

These items hold consistent measurements, easily counted and grouped by multiples of their unit size, like counting building blocks.

When looking at volumes that are quantized, it's equivalent to observing how digital clocks tick at fixed intervals versus continuously flowing time on an analog clock. Discrete volume offers predictability and uniformity, aiding in both packaging and sales planning.

Continuous Volume

Unlike discrete volume, continuous volume refers to liquid quantities that can be any value—without restriction to set multiples. Consider a drinking fountain.

You can take as little or as much water as you want, adjusting the amount with no strict divisions.

• A drinking fountain
• A soda-fountain dispenser

These are examples where you control the flow and by extension, the volume you eventually have.

The continuous volume is like a line that can stretch infinitely at any point, offering flexibility and variation. In real-world scenarios, these systems provide more adaptability to the needs of the user, unlike set volumes which impose limitations.

This form of measurement stems from the fundamentally unlimited natural world, catering to a variety of purposes where precision isn't determined by pre-set forms or portions.

Measurement in Chemistry

Measurement in chemistry often involves dealing with both discrete and continuous volumes.

When chemists measure liquids, they may use tools that determine specific quantities, like a graduated cylinder, or require precise portions, like pipettes for titration.

• Graduated cylinders for accurate readings
• Flasks for continuous mixing

These measurements are critical for reactions, where the balance between reactants can mean the difference in successful outcomes.

Understanding the type of volume being measured aids in ensuring accuracy. Measuring discrete volumes can be vital when specific reactions require exact amounts, while continuous volumes might be valuable when adjusting reaction conditions on the fly. Using proper measurement tools aligns with various experimental needs, ensuring efficacy in scientific explorations and industrial applications.