Problem 26 - Chemistry and Chemical Reactivity

Question

Some soft drinks are sold in bottles with a volume of \(1.5 \mathrm{L}\) What is this volume in milliliters? In cubic centimeters? In cubic decimeters?

Step-by-Step Solution

Answer

The volume is 1500 mL, 1500 cm³, and 1.5 dm³.

Step 1: Convert Liters to Milliliters

To convert liters to milliliters, use the conversion factor where 1 liter (L) equals 1000 milliliters (mL). Therefore, multiply 1.5 liters by 1000 milliliters per liter: \[1.5 ext{ L} imes 1000 ext{ mL/L} = 1500 ext{ mL}\]So, the volume is 1500 milliliters.

Step 2: Convert Liters to Cubic Centimeters

Since 1 milliliter is equal to 1 cubic centimeter (cm³), the volume in milliliters is the same as the volume in cubic centimeters. Therefore, 1500 milliliters equals 1500 cubic centimeters: \[1500 ext{ mL} = 1500 ext{ cm}^3\]The volume is 1500 cubic centimeters.

Step 3: Convert Liters to Cubic Decimeters

1 liter is equivalent to 1 cubic decimeter (dm³). Therefore, the volume in liters is directly equal to the volume in cubic decimeters: \[1.5 ext{ L} = 1.5 ext{ dm}^3\]The volume is 1.5 cubic decimeters.

Key Concepts

Liters to Milliliters

To convert liters to milliliters, you simply need to know the basic conversion factor between these two units. In the metric system, which is used to measure volume, 1 liter (L) is equal to 1000 milliliters (mL). This relationship is straightforward and helpful for any kind of volume conversion.

For example, if you have a beverage bottle that contains 1.5 liters, converting it to milliliters is simple. Just multiply the volume in liters by 1000:

• The formula is: \[ 1.5 \text{ L} \times 1000 \frac{\text{mL}}{\text{L}} = 1500 \text{ mL} \]

This means your bottle contains 1500 milliliters of liquid. Remember, multiplying by 1000 is all it takes to switch from liters to milliliters!

Liters to Cubic Centimeters

The conversion from liters to cubic centimeters (cm³) is another simple task once you know the basic relationships in metric volume measurements. A crucial point to note is that 1 milliliter (mL) is equivalent to 1 cubic centimeter (cm³). This means that the volume in milliliters is the same as the volume in cubic centimeters.

So, if you already have your volume in milliliters, converting to cubic centimeters is a breeze. Using our previous example of a 1.5-liter bottle, which we determined to be 1500 milliliters, you can say:

• \[ 1500 \text{ mL} = 1500 \text{ cm}^3 \]

When you think about it, milliliters and cubic centimeters are really interchangeable terms for most basic calculations. So, next time you see volume in one of these units, you can easily convert it without any extra steps!

Liters to Cubic Decimeters

Converting liters to cubic decimeters (dm³) might look daunting, but it’s actually the simplest conversion of the bunch because the two units are equivalent. This means that 1 liter (L) is exactly the same volume as 1 cubic decimeter (dm³).

This direct relationship allows you to transfer the same numerical value from liters to cubic decimeters without any calculations. Here’s how it works with our 1.5-liter example:

• You directly have: \[ 1.5 \text{ L} = 1.5 \text{ dm}^3 \]

Whenever you need to convert between these two units, you can confidently state that the volume in liters is the same as the volume in cubic decimeters without additional computation. This makes things super straightforward!