Question

Use the density value to solve the following problems: a. What is the mass, in grams, of \(150 \mathrm{~mL}\) of a liquid with a density of \(1.4 \mathrm{~g} / \mathrm{mL}\) ? b. What is the mass of a glucose solution that fills a \(0.500\) -L intravenous bottle if the density of the glucose solution is \(1.15 \mathrm{~g} / \mathrm{mL} ?\) c. A sculptor has prepared a mold for casting a bronze figure. The figure has a volume of \(225 \mathrm{~mL}\). If bronze has a density of \(7.8 \mathrm{~g} / \mathrm{mL}\), how many ounces of bronze are needed in the preparation of the bronze figure?

Short answer

a. 210 gb. 575 gc. 61.92 oz

Step-by-step solution

Problem Analysis and Formula

The general formula to find mass from density and volume is given by: \[ \text{mass} = \text{density} \times \text{volume} \]We will apply this formula to each part of the problem.

Calculate Mass for Part (a)

For the liquid: Given: Density = \(1.4 \, \mathrm{g/mL}\)Volume = \(150 \, \mathrm{mL}\)Using the formula: \[ \text{mass}_{\text{(a)}} = 1.4 \, \mathrm{g/mL} \times 150 \, \mathrm{mL} \]Calculation: \[ \text{mass}_{\text{(a)}} = 210 \, \mathrm{g} \]

Calculate Mass for Part (b)

For the glucose solution: Given: Density = \(1.15 \, \mathrm{g/mL}\)Volume = \(0.500 \, \mathrm{L}\) (convert to mL: \(0.500 \, \mathrm{L} = 500 \, \mathrm{mL}\))Using the formula: \[ \text{mass}_{\text{(b)}} = 1.15 \, \mathrm{g/mL} \times 500 \, \mathrm{mL} \]Calculation: \[ \text{mass}_{\text{(b)}} = 575 \, \mathrm{g} \]

Calculate Mass for Part (c) and Convert to Ounces

For the bronze figure: Given: Density = \(7.8 \, \mathrm{g/mL}\)Volume = \(225 \, \mathrm{mL}\)Using the formula: \[ \text{mass}_{\text{(c)}} = 7.8 \, \mathrm{g/mL} \times 225 \, \mathrm{mL} \]Calculation: \[ \text{mass}_{\text{(c)}} = 1755 \, \mathrm{g} \]To convert grams to ounces: 1 gram = 0.035274 ounces\[ \text{mass}_{\text{(c)}, \text{oz}} = 1755 \, \mathrm{g} \times 0.035274 \, \mathrm{oz/g} \]Calculation: \[ \text{mass}_{\text{(c)}, \text{oz}} = 61.92 \, \mathrm{oz} \]

Key concepts

density formula

The density formula is a fundamental concept in physics and chemistry that connects mass and volume. The formula is given by: \[ \text{mass} = \text{density} \times \text{volume} \] In this equation:

• Mass is the amount of matter in the object, typically measured in grams (\text{g}).
• Density is the mass per unit volume of a substance, expressed in grams per milliliter (\text{g/mL}).
• Volume is the space that the object occupies, commonly measured in milliliters (\text{mL}) or liters (\text{L}).

The formula reveals that if you know the density and volume of a material, you can easily calculate its mass. For instance, if you have a liquid with a density of 1.4 \text{g/mL} and a volume of 150 \text{mL}, you just multiply these values to get the mass. Simple, right? This fundamental relationship is a powerful tool and is widely used in various scientific calculations.

mass calculation

Calculating mass using the density formula involves straightforward arithmetic. Let's take a closer look at how it's done: \[ \text{mass} = \text{density} \times \text{volume} \]

Part (a): Given that the density of a liquid is 1.4 \text{g/mL}, and its volume is 150 \text{mL}, we find the mass as follows:
\[ \text{mass}_{\text{(a)}} = 1.4 \text{g/mL} \times 150 \text{mL} = 210 \text{g} \]

Part (b): For a glucose solution with a density of 1.15 \text{g/mL} and a volume of 0.500 \text{L}, first convert the volume to milliliters:
\[ 0.500 \text{L} = 500 \text{mL} \] Then calculate the mass:
\[ \text{mass}_{\text{(b)}} = 1.15 \text{g/mL} \times 500 \text{mL} = 575 \text{g} \]

Part (c): To find the mass of a bronze figure with a density of 7.8 \text{g/mL} and a volume of 225 \text{mL}:
\[ \text{mass}_{\text{(c)}} = 7.8 \text{g/mL} \times 225 \text{mL} = 1755 \text{g} \] This step-by-step process simplifies mass calculation using given density and volume values.

unit conversion

Unit conversion is often necessary in mass calculations to ensure all units are compatible. Here's a closer look at converting units:

• Volume Conversion: Sometimes, volume is given in liters (L) but needs to be in milliliters (mL) for mass calculation. Remember, 1 L = 1000 mL. For example, 0.500 L is converted to 500 mL.
• Mass Conversion: Calculated mass might need to be in different units. Commonly, conversions between grams (g) and ounces (oz) are required. The conversion factor is: \[ 1 \text{gram} = 0.035274 \text{ounces} \] Using this factor, you can easily convert grams to ounces. For example, if the mass is 1755 g, it converts to ounces as follows: \[ \text{mass}_{\text{(c)}, \text{oz}} = 1755 \text{g} \times 0.035274 \text{oz/g} = 61.92 \text{oz} \]

Unit conversion ensures the calculated mass matches the desired units, simplifying the use of data in real-world applications.