Problem 25 - Chemistry and Chemical Reactivity

Question

A typical laboratory beaker has a volume of \(250 .\) mL. What is its volume in cubic centimeters? In liters? In cubic meters? In cubic decimeters?

Step-by-Step Solution

Answer

250 cm³, 0.25 L, 0.00025 m³, 0.25 dm³.

Step 1: Volume Conversion to Cubic Centimeters

A milliliter (mL) is equivalent to a cubic centimeter (cm extsuperscript{3}). Therefore, the volume of the beaker is already given as 250 cm extsuperscript{3}.

Step 2: Volume Conversion to Liters

One liter (L) is equal to 1000 milliliters (mL). To convert 250 mL to liters, divide by 1000: \( \frac{250}{1000} = 0.25 \) L.

Step 3: Volume Conversion to Cubic Meters

One cubic meter (m extsuperscript{3}) is equal to 1,000,000 cubic centimeters (cm extsuperscript{3}). To convert 250 cm extsuperscript{3} to m extsuperscript{3}, divide by 1,000,000: \( \frac{250}{1,000,000} = 0.00025 \) m extsuperscript{3}.

Step 4: Volume Conversion to Cubic Decimeters

One cubic decimeter (dm extsuperscript{3}) is equal to one liter. Since we already converted the volume to liters as 0.25 L, it is the same value in cubic decimeters: 0.25 dm extsuperscript{3}.

Key Concepts

Cubic Centimeters to Liters

Understanding the conversion from cubic centimeters (cm³) to liters is important when exploring volume measurements in the metric system. Since 1 liter is equivalent to 1,000 milliliters (mL) and one milliliter is exactly equivalent to one cubic centimeter, the process of converting from cubic centimeters to liters is straightforward. All you have to do is divide the number of cubic centimeters by 1,000.

Let's consider you have a volume of 250 cm³. To find out how many liters that is, you calculate: \[\frac{250 \text{ cm}^3}{1000} = 0.25 \text{ L}\]
This tells us that 250 cubic centimeters equals 0.25 liters. This conversion is particularly useful in fields such as chemistry, where smaller quantities are often measured in cubic centimeters before scaling up to liters.

Liters to Cubic Meters

To convert liters to cubic meters, it's essential to grasp the relationship between these two units of volume. One cubic meter (m³) is an equivalent of 1,000 liters. This conversion is often needed in scenarios where large volumes need to be expressed in more manageable numbers, like industrial storage or tank capacities.

For example, if you know you have a volume of 0.25 liters and you need to express it in cubic meters, you would calculate:\[\frac{0.25 \text{ L}}{1000} = 0.00025 \text{ m}^3\]This equation shows that 0.25 liters is equivalent to 0.00025 cubic meters. Converting between these units makes it easier to visualize and work with different scales of volume.

Cubic Meters to Cubic Decimeters

The conversion between cubic meters and cubic decimeters is a common task in measurement, especially when dealing with water or other fluids. Importantly, 1 cubic meter is equal to 1,000 cubic decimeters. This conversion is rooted in the definition of the liter, which occupies the same volume as one cubic decimeter.

Considering a previously converted volume, if you have 0.00025 cubic meters, you can determine how many cubic decimeters this is by multiplying by 1,000:\[0.00025 \text{ m}^3 \times 1000 = 0.25 \text{ dm}^3\]Hence, 0.00025 cubic meters is equal to 0.25 cubic decimeters. Understanding these conversions is particularly handy in various scientific calculations, where interpreting data across different units is often necessary.