Question

A rectangular solid measures \(1.0 \mathrm{~m}\) by \(2.4 \mathrm{~mm}\) by \(3.9 \mathrm{dm} .\) What is the volume in liters?

Short answer

The volume of the rectangular solid is approximately \(0.936\) liters.

Step-by-step solution

Convert all dimensions to meters.

First, we need to convert the given dimensions into meters. We have: - 1.0 m (already in meters) - 2.4 mm = 0.0024 m (1 mm = 0.001 m) - 3.9 dm = 0.39 m (1 dm = 0.1 m)

Calculate the volume in cubic meters.

Now, we can find the volume of the solid. The volume of a rectangular solid is equal to the product of its length, width, and height. In this case, we have: Volume = length × width × height = 1.0 m × 0.0024 m × 0.39 m = 0.000936 m³

Convert the volume to liters.

Finally, we need to convert the volume from cubic meters to liters. We know that 1 m³ = 1,000 L. Therefore: Volume = 0.000936 m³ × (1,000 L/1 m³) = 0.936 L The volume of the rectangular solid is approximately 0.936 liters.

Key concepts

Unit Conversion

Understanding unit conversion is crucial in the study of chemistry and other sciences. It is the process of changing one unit of measurement to another without changing the quantity. In chemistry, this is essential for measuring substances, analyzing reaction rates, and carrying out experiments.

In the given exercise, we convert dimensions of a solid from millimeters and decimeters into meters to maintain consistency before calculating its volume. Knowing that 1 mm is equal to 0.001 m and 1 dm is equal to 0.1 m, we can easily perform these conversions. For accuracy in science, it is vital to master unit conversion, as small miscalculations can lead to significantly different results.

Common Conversion Factors

• Length: 1 cm = 0.01 m, 1 mm = 0.001 m, 1 km = 1,000 m
• Volume: 1 mL = 0.001 L, 1 cubic meter = 1,000 L
• Mass: 1 kg = 1,000 g, 1 mg = 0.001 g

Remembering key conversion factors and how to use them can significantly simplify problem-solving in chemistry.

Rectangular Solid Volume

Calculating the volume of a rectangular solid, which is a three-dimensional figure with six rectangular faces at right angles to each other, is straightforward once you know its length, width, and height. The formula for the volume is: \[\text{Volume} = \text{length} \times \text{width} \times \text{height}\]In our exercise, after the conversion of the units to meters, the volume of the solid was found by multiplying the converted dimensions. Volume calculations like this are important not only in chemistry but in many fields including engineering, construction, and agriculture.

Understanding the geometrical principles behind these calculations can provide a better grasp of the physical world and help in visualizing molecular structures and reaction vessels in chemistry.

Metric System

The metric system, also known as International System of Units (SI), is the standard system of measurement used in science. This system is based on multiples of ten, which makes it straightforward to convert between units, as seen in the exercise. The metric system is important because it provides a universal language for scientists around the world, enabling them to compare findings and conduct experiments with standard units.

Key base units in the metric system include the meter for length, the liter for volume, and the gram for mass. Prefixes like milli-, centi-, and kilo- represent various scales of measurements. Understanding and using the metric system effectively allows students and scientists to communicate more efficiently and to approach problems methodically.

Benefits of the Metric System

• Simplicity: Uses powers of ten for easy conversion
• Universality: Widely adopted in scientific communities
• Precision: Facilitates accurate measurements and calculations

Embracing the metric system is therefore a foundational skill for success in chemistry and other scientific disciplines.