Problem 27 - General Chemistry: Principles and Modern Applications

Question

Perform the following conversions. (a) \(0.127 \mathrm{L}=\)_________\(\mathrm{mL}\) (b) \(15.8 \mathrm{mL}=\)_________\(\mathrm{L}\) (c) \(2896 \mathrm{mm}=\)__________\(\mathrm{L}\) (d) \(2.65 \mathrm{m}^{3}=\)__________\(\mathrm{cm}^{3}\)

Step-by-Step Solution

Answer

(a) 127 mL, (b) 0.0158 L, (c) 2.896 L, (d) 2,650,000 cm³

Step 1: Converting liters to milliliters

1 liter is equivalent to 1000 milliliters. Therefore, to convert liters to milliliters, you multiply the given value by 1000. In this case, \(0.127 L\) is equal to \(0.127 L * 1000 = 127 mL\).

Step 2: Converting milliliters to liters

1 milliliter equals 0.001 liters. Therefore, to convert milliliters to liters, you multiply the given value by 0.001. Therefore, \(15.8 mL\) is equal to \(15.8 mL * 0.001 = 0.0158 L\).

Step 3: Converting millimeters to liters

1 cubic millimeter equals 0.000001 liters. Therefore, to convert cubic millimeters to liters, you multiply the given value by 0.000001. Therefore, \(2896 mm³\) is equal to \(2896 mm³ * 0.000001 = 2.896 L\).

Step 4: Converting meters cubed to centimeters cubed

1 cubic meter (m³) is equivalent to 1,000,000 cubic centimeters (cm³). So to convert from cubic meters to cubic centimeters, the given value is multiplied by 1,000,000. Therefore, \(2.65 m³\) is equal to \(2.65 m³ * 1,000,000 = 2,650,000 cm³\).

Key Concepts

Liters to Milliliters Conversion

To convert liters to milliliters, it's important to remember the basic relationship: 1 liter is equal to 1000 milliliters. This is a core conversion concept that will help you handle a wide range of exercises and real-life situations, such as measuring liquid volumes.

The conversion process is straightforward. If you have a value in liters and need to convert it to milliliters, simply multiply it by 1000. For example, if you have 0.127 liters, you multiply it by 1000 to get 127 milliliters. This is because:

• 1 L = 1000 mL
• 0.127 L × 1000 = 127 mL

This relationship is useful in many practical scenarios, especially in industries like cooking or pharmaceuticals, where precision is key. Feel free to use this formula whenever you need a second opinion on measurements!

Milliliters to Liters Conversion

When converting milliliters to liters, you simply use the inverse of the relationship found in the liters to milliliters conversion. Remember, 1 milliliter is equal to 0.001 liters. This conversion is particularly handy when you're dealing with small quantities of liquid.

To perform the conversion, you multiply the milliliters value by 0.001. So, if you have 15.8 milliliters and want to find out how many liters that is, your calculation would be:

• 1 mL = 0.001 L
• 15.8 mL × 0.001 = 0.0158 L

This type of conversion is essential in various fields such as science labs and medical dosing, where concentrations are often calculated in liters.

Cubic Meters to Cubic Centimeters Conversion

Converting cubic meters to cubic centimeters is a frequently used conversion in fields that involve volume measurement, like construction and architecture. This conversion requires you to know that 1 cubic meter is equivalent to 1,000,000 cubic centimeters. It's a powerful conversion when dealing with large capacities, ensuring precise volume calculations.

To convert from cubic meters to cubic centimeters, you multiply the given value in cubic meters by 1,000,000. For instance, consider how you'd convert 2.65 cubic meters to cubic centimeters:

• 1 m³ = 1,000,000 cm³
• 2.65 m³ × 1,000,000 = 2,650,000 cm³

This conversion is indispensable for designing spaces or crafting detailed engineering plans, ensuring that dimensions are accurately scaled.