(a) What is the mass of a silver cube whose edges measure 2.00 cm each at 25^∘ C ? The density o

(a) What is the mass of a silver cube whose edges measure...

(a) What is the mass of a silver cube whose edges measure 2.00 $\mathrm{cm}$ each at $25^{\circ} \mathrm{C} ?$ The density of silver is $10.49 \mathrm{~g} / \mathrm{cm}^{3}$ at $25^{\circ} \mathrm{C}$. (b) The density of aluminum is $2.70 \mathrm{~g} / \mathrm{cm}^{3}$ at $25^{\circ} \mathrm{C}$. What is the weight of the aluminum foil with an area of $0.5 \mathrm{~m}^{2}$ and a thickness of $0.5 \mathrm{~mm} ?$ (c) The density of hexane is $0.655 \mathrm{~g} / \mathrm{mL}$ at $25^{\circ} \mathrm{C} .$ Calculate the mass of $1.5 \mathrm{~L}$ of hexane at this temperature.

(a) What is the mass of a silver cube whose edges measure 2.00 $\mathrm{cm}$ each at $25^{\circ} \mathrm{C} ?$ The density of silver is $10.49 \mathrm{~g} / \mathrm{cm}^{3}$ at $25^{\circ} \mathrm{C}$.
(b) The density of aluminum is $2.70 \mathrm{~g} / \mathrm{cm}^{3}$ at $25^{\circ} \mathrm{C}$. What is the weight of the aluminum foil with an area of $0.5 \mathrm{~m}^{2}$ and a thickness of $0.5 \mathrm{~mm} ?$ (c) The density of hexane is $0.655 \mathrm{~g} / \mathrm{mL}$ at $25^{\circ} \mathrm{C} .$ Calculate the mass of $1.5 \mathrm{~L}$ of hexane at this temperature.

Key Concepts

Weight vs. Mass

The weight of an object is the force exerted on it due to gravity and is calculated by multiplying its mass by the acceleration due to gravity. In contexts where weight is requested rather than mass, it is important to perform this conversion to account for gravitational force. Understanding the difference between weight (a force) and mass (a measure of matter) is crucial in physics and engineering applications.

Unit Conversion

Unit conversion is the process of converting quantities expressed in one set of units to another, ensuring consistency when performing calculations. This includes converting measurements like cm³ to mL (which are equivalent for water-based calculations), turning millimeters into centimeters or meters for thickness, and converting liters to milliliters when calculating the volume of liquids. Accurate conversion is essential for correct application of formulas in practical problems.

Volume Calculation

Volume calculation involves determining the space occupied by a three-dimensional object. For regular solids like cubes or thin foils, the volume can be computed using specific geometric formulas. For a cube, the volume is the edge length cubed, while for flat objects like foils, the volume is found by multiplying the area by the thickness.

Density

Density is defined as the mass per unit volume of a substance and is typically expressed in units such as g/cm³ or g/mL. In these problems, the density is used to calculate the mass of a material when its volume is known by multiplying the density by the volume. It is a fundamental property that connects the physical makeup of a material to its mass and volume.

Transcript

00:01 If we have a silver cube, it's our silver cube here, who's each edge or side, so we'll have these edges or sides.

00:11 So each one of these measures two centimeters at 25 degrees celsius.

00:32 And we also know that the density of silver, so we have the density is equal to 10, 0 .49 grams per cubic centimeter.

00:57 And we want to know what the mass will be of our cube with each side equal to, their side equal to two centimeters.

01:11 Okay, so if we have each side, and we know that the volume of a cube is sides cubed, so you can do two cubed, which equals 8 centimeters for our volume.

01:29 8 cubic centimeters will be our volume.

01:33 So if we have the density of silver and we have the volume, we can use the equation for density to find the mass.

01:43 And the equation for density is just t equal to mass over volume.

01:49 Okay, so we have our density at 10 .49 grams.

01:57 Per cubic centimeter equal to our mass which we want to find over our volume eight cubic centimeters.

02:07 So you can multiply both sides by eight here.

02:15 And we get, let's not going to cross up, but yeah, we get our mass is equal to 83 .92 grams.

02:37 Now we're given the density of aluminum.

02:41 The density of aluminum equals 2 .7 grams per cubic centimeter and we're also given the area in the thickness.

03:01 Okay, so with this information we have a density and we have area and thickness.

03:08 With these we can make volume, right? except they're in different units and our density is in centimeters so it'd be easiest to convert these to centimeters so we could use them in our density equation to find the mass.

03:23 Okay, so we'll do that first.

03:27 We will turn 0 .5 meters into centimeters.

03:32 So to get our area to centimeters, we'll multiply it by 100...

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