Problem 3 - Chemistry: Introducing Inorganic, Organic and Physical Chemistry

Question

A sealed flask holds \(10 \mathrm{dm}^{3}\) of gas. What is this volume in (a) \(\left.\mathrm{cm}^{3},(\mathrm{b}) \mathrm{m}^{3}, \text { (c) litres? (Section } 1.2\right)\)

Step-by-Step Solution

Answer

(a) 10,000 cm³, (b) 0.01 m³, (c) 10 liters

Step 1: Convert to Cubic Centimeters

1 decimeter (dm) is equal to 10 centimeters (cm). Since the flask holds 10 dm³ of gas, and we know that 1 dm³ equals 1000 cm³, we can find the volume in cm³ by multiplying:\[\text{Volume in cm}^3 = 10 \, \text{dm}^3 \times 1000 \, \text{cm}^3/\text{dm}^3 = 10,000 \, \text{cm}^3\]

Step 2: Convert to Cubic Meters

1 cubic meter (m³) is equal to 1000 cubic decimeters (dm³). To find the volume in cubic meters, divide the volume in dm³ by 1000:\[\text{Volume in m}^3 = \frac{10 \, \text{dm}^3}{1000 \, \text{dm}^3/\text{m}^3} = 0.01 \, \text{m}^3\]

Step 3: Convert to Liters

1 liter (L) is equivalent to 1 cubic decimeter (dm³). Therefore, the volume in liters is the same as the volume in dm³:\[\text{Volume in liters} = 10 \, \text{dm}^3 = 10\, \text{liters}\]

Key Concepts

Cubic Centimeters

The cubic centimeter, often abbreviated as cc or cm³, is a unit of volume commonly used to measure small quantities. It is particularly prevalent in medical dosages and engine capacities. One cubic centimeter is the volume of a cube with edges of one centimeter. Since it is a smaller unit of measurement, it is highly suitable for precise calculations.

Understanding how to convert other volume measurements to cubic centimeters is crucial. For instance, converting from decimeters to centimeters involves knowing that 1 dm equals 10 cm. Therefore, since 1 cubic decimeter ( m³) is equivalent to 10 x 10 x 10 = 1000 cm³, calculations become straightforward.

• Example: Remember that 1 dm³ = 1000 cm³ and 10 dm³ = 10,000 cm³.
• This conversion multiplier of 1000 is essential for the switch between dm³ to cm³.

Cubic centimeters offer better precision for smaller volume calculations, making it invaluable in scientific and everyday scenarios.

Cubic Meters

Cubic meters, represented as m³, is a unit of volume in the International System of Units (SI) and is typically used to express large volumes, such as the capacity of a tank or the flow rate of water. One m³ is the volume of a cube with edges that are one meter long. This unit is ideal for volumetric measurements on a larger scale, providing a clear sense of spatial magnitude.

To convert from cubic decimeters to cubic meters, recall that 1 m³ equals 1000 dm³. Therefore, dividing the number of cubic decimeters by 1000 will give the volume in cubic meters.

• Example: If you have 10 dm³, dividing by 1000 results in 0.01 m³.
• This conversion process is helpful for understanding large-scale quantities in industries like construction or manufacturing.

In essence, cubic meters facilitate comprehension and communication concerning larger volume measures.

Liters

The liter (L) is a unit of volume commonly used in daily life, from measuring liquids like beverages to expressing fuel quantities in vehicles. A key concept to understand is that 1 liter is precisely the same as 1 cubic decimeter (dm³). This makes conversion between these two units exceptionally straightforward.

For example, when you know the volume in cubic decimeters, you simultaneously know it in liters without any further calculation.

• Example: 10 dm³ equals 10 liters.
• This equivalency is critical because many fluid measurements in cooking, chemistry, and beyond are recorded in liters.

Understanding that 1 dm³ is equivalent to 1 liter can reduce conversion complexity and allows for seamless utilization in everyday and scientific contexts.