Question

Will a hollow cube with sides of length \(0.50 \mathrm{~m}\) hold \(8.5 \mathrm{~L}\) of solution? Depending on your answer, how much additional solution would be required to fill the container or how many times would the container need to be filled to measure the \(8.5 \mathrm{~L}\) ?

Short answer

The hollow cube will hold the solution. It will remain underfilled by 116.5 L.

Step-by-step solution

Calculate the volume of the cube

The volume of a cube is calculated using the formula \( V = s^3 \), where \( s \) is the side length of the cube. Substitute the given side length: \( V = (0.50 \, m)^3 \).

Perform the cube calculation

Calculate the volume: \( V = 0.50 \, m \times 0.50 \, m \times 0.50 \, m \). This results in \( V = 0.125 \, m^3 \).

Convert the volume to liters

1 cubic meter is equivalent to 1000 liters. Therefore, \( 0.125 \, m^3 = 0.125 \times 1000 \, L = 125 \, L \).

Compare the volume of the cube to the solution volume

The volume of the hollow cube is \( 125 \, L \) and the required volume of solution is \( 8.5 \, L \). Since \( 125 \, L \) is greater than \( 8.5 \, L \), the hollow cube can hold the solution.

Calculate the additional solution required or the number of times to fill the container

Since the hollow cube can hold up to \( 125 \, L \) and we only need \( 8.5 \, L \), we don't need to fill the cube multiple times. Instead, we should calculate how much the hollow cube is underfilled. The remaining capacity will be \( 125 \, L - 8.5 \, L = 116.5 \, L \).

Key concepts

Unit Conversion

Understanding unit conversion is crucial for solving many chemistry problems.
In this exercise, it's essential to convert between cubic meters and liters to compare the cube's volume with the given volume of the solution.
Here's a quick guide:

• 1 cubic meter (m³) equals 1000 liters (L).
. To convert cubic meters to liters, simply multiply by 1000. For example, \[0.125 \, m^3 \times 1000 \, L \,/ \, m^3 = 125 \, L\]. This conversion shows how much solution the cube can hold.
Unit conversion helps in understanding various measures and applying them in real problems.
Grasping this can make complex chemistry problems easier.

Volume of Solids

Calculating the volume of solids is a fundamental concept in chemistry.
For a cube, the volume is determined using the formula \[V = s^3\].
Here, \[s\] is the length of any side of the cube.
In the given problem:

• Side length (\[s\]) = 0.50 m
• Volume (\[V\]) = \[0.50 \, m \, \times \, 0.50 \, m \, \times \, 0.50 \, m = 0.125 \, m^3\]

This result shows that the cube has a volume of 0.125 cubic meters.
By converting this to liters, we find it can hold 125 liters of solution.
Understanding the volume of solids helps in many real-world applications, such as container capacity and material quantity calculations.

Problem Solving in Chemistry

Chemistry often requires carefully following steps to solve problems.
Let's break down the problem-solving process in this exercise:

• Step 1: Calculate the volume of the hollow cube using the given side length and cube volume formula.
• Step 2: Perform the multiplication to find that \[0.50 \, m \, \times \, 0.50 \, m \, \times \, 0.50 \, m = 0.125 \, m^3\].
• Step 3: Convert cubic meters to liters (as 1 cubic meter = 1000 liters) resulting in 125 liters.
• Step 4: Compare the cube's volume (125 liters) to the solution volume (8.5 liters) and determine the cube can hold the solution.
• Step 5: Calculate the additional solution required (if needed). Here, the cube has more than enough space, leaving us with an extra capacity of 116.5 liters.
  These clear, step-by-step approaches are vital in chemistry, making problem-solving more manageable.