Question

Liquid A is made of water, alcohol and bleach in the ratio of \(3: 1: 2\). Liquid \(\mathrm{B}\) is made of water, alcohol and bleach in the ratio \(4: 2: 1\). (a) If equal volumes of liquids A and B are mixed, calculate the ratio of water, alcohol and bleach in the new liquid. (b) If liquid A and liquid B are mixed in the ratio \(2: 1\), calculate the ratio of water, alcohol and bleach in the resulting mix.

Short answer

Answer: When mixed in equal volumes, the ratio of water, alcohol, and bleach in the new liquid is 7:3:3. When mixed in a 2:1 ratio, the ratio of water, alcohol, and bleach in the new liquid is 10:4:5.

Step-by-step solution

Identify the Ratios of Components in Each Liquid Separately

Liquid A has a ratio of \(3:1:2\), which represents the ratio of water, alcohol, and bleach respectively in the liquid. Similarly, Liquid B has a ratio of \(4:2:1\).

Mixing Equal Volumes of Liquid A and B (Part A)

Let the equal volumes of Liquid A and B be \(c\). Now we will find the amount of each component in the mixed liquid. Amount of water in the new liquid = \(3c + 4c = 7c\) Amount of alcohol in the new liquid = \(1c + 2c = 3c\) Amount of bleach in the new liquid = \(2c + 1c = 3c\) The ratio of water, alcohol, and bleach in the new liquid is \(7:3:3\).

Mixing Liquid A and B in the Ratio 2:1 (Part B)

Let the volume of Liquid A be \(2d\) and that of Liquid B be \(d\). Now, we will find the amount of each component in the mixed liquid. Amount of water in the new liquid = \((3 \times 2d) + (4 \times d) = 6d + 4d = 10d\) Amount of alcohol in the new liquid = \((1 \times 2d) + (2 \times d) = 2d + 2d = 4d\) Amount of bleach in the new liquid = \((2 \times 2d) + (1 \times d) = 4d + d = 5d\) The ratio of water, alcohol, and bleach in the new liquid is \(10:4:5\).

Key concepts

Liquid Mixtures

Liquid mixtures involve combining different liquids, each of which is composed of various substances in specific ratios. In this particular exercise, Liquid A consists of water, alcohol, and bleach mixed in the ratio of 3:1:2. Liquid B, on the other hand, contains these substances in a ratio of 4:2:1. These ratios determine the proportion of each component within the liquid. When understanding liquid mixtures, it's essential to focus on how the components interact when combined. For example:

• Water, as a universal solvent, has unique properties that can influence the final concentration of the mixture.
• Alcohols, due to their volatility, may impact the evaporation rate of a mixture.
• Bleach, being a reactive substance, can affect the chemical stability of the mixture.

The goal of examining these mixtures is mainly to predict the outcome of their interaction, such as pH balances, potency, and color.

Arithmetic Operations

Arithmetic operations play a crucial role when working with ratios and mixing liquids. To solve problems involving liquid mixtures, you will frequently rely on basic arithmetic operations such as addition and multiplication. This exercise involves calculating the amounts of each component after mixing the liquids in various scenarios. Let's break down the operations:

• Addition: Used to combine the components of two mixtures. For instance, when combining water from Liquid A and B, you add their respective ratios together.
• Multiplication: Applied when adjusting proportions. For example, if two parts of Liquid A are mixed with one part of Liquid B, each ratio must be multiplied by the respective volume.

Understanding these operations is key to accurately determining the ratios of components in new mixtures. It's all about maintaining consistency in calculations from start to finish.

Proportion Calculations

Proportion calculations are vital for determining how different quantities relate within liquid mixtures. When mixing liquids, it's necessary to keep the proportions consistent to ensure the final product has the desired properties. This exercise involves calculating the resulting ratio when equal volumes and specified ratios of two liquids are blended. Here’s a look into the process:

• In part (a), equal volumes are considered, making the calculations straightforward, as you simply add the component ratios.
• In part (b), where a 2:1 mixing ratio is employed, the number of parts given for each liquid must be multiplied with the volumes they represent, making it slightly more complex.

By practicing these calculations, you'll learn to effortlessly balance and adjust proportions, which is crucial in fields such as chemistry and culinary arts where mixtures are fundamental.