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Calculate the mass of each of the following: (a) a sphere of gold with a radius of $10.0 \mathrm{cm}$ [the volume of a sphere with a radius $r$ is $V=(4 / 3) \pi r^{3} ;$ the density of gold $\left.=19.3 \mathrm{g} / \mathrm{cm}^{3}\right],$ (b) a cube of platinum of edge length $0.040 \mathrm{mm}$ (the density of platinum $=$ $\left.21.4 \mathrm{g} / \mathrm{cm}^{3}\right),(\mathrm{c}) 50.0 \mathrm{mL}$ of ethanol (the density of ethanol $=0.798 \mathrm{g} / \mathrm{mL}).$

mass $=$density $\times$ volume

Chemistry 101

Chapter 1

Chemistry: The Study of Change

Intro to Chemistry

University of Central Florida

Rice University

University of Maryland - University College

Brown University

Lectures

02:29

Chemistry is the science of matter, especially its chemical reactions, but also its composition, structure and properties. Chemistry deals with atoms and their interactions with other atoms, and particularly with the properties of chemical bonds. Chemistry also involves understanding the properties and interactions of individual atoms and molecules for use in larger-scale applications.

04:42

In chemistry and physics, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic particles, and in everyday as well as scientific usage, "matter" generally includes atoms and anything made up of them, and any particles and objects that act as if they have both rest mass and volume. However it does not include massless particles such as photons, or other energy phenomena or waves such as light or sound. Matter exists in various states (known as phases) that are defined by various physical properties, such as state of matter, phase, shape, and density. The Standard Model of particle physics and the general theory of relativity describe fundamental particles and the fundamental forces acting between them that control the structure and dynamics of matter.

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Calculate the mass of each…

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1.59Calculate the mass…

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The density of gold is 19.…

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(a) You are given a cube o…

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The density of gold is $19…

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(a) Three spheres of equal…

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Hi. This question is asking. You just calculate massive following substances that they give you a particular measurement force. You can find the volume, and then they give you the density. So a very important question equation we're gonna have to know for all three of these parts is the mass density volume equation. So we have mass equals intensity times, William, and this makes sense because density is the mass per unit volume, right? So if I have a particular mass per unit volume, I could multiply that by the volume to get the total mass of that substance. Okay, so we can see this in practice Part A, where we have a sphere gold with the radius of 10.0 centimeters to give you the volume equation, which is V equals 4/3 pi r cubed and the density of gold, which is 19.3 grounds per centimeters acute. So first we gotta make sure is that our units are the same for the radius and the gold, so we can cancel of the density of gold so we can cancel it out. They're both centimeters, so that works out just fine. So let's find the volume. First volume equals 4/3. Hi are huge. And are in this case is the radius to give us right 7.0 para three. So 4/3 pi tented part three she get 4000 189 centimetres cute unnoticed that I use force a fix here because I'm generally an intermediate steps like this one. You want to use force a fix? You don't get a lot around here, even though my initial value is only 36 pigs. But for my answer, I'm only gonna wanna have 36 years. Okay, let's see now for the next part. We have mass equals density times volume. Right. So we're gonna use the density they gave us, which is 19.3 grams per centimeter. Huge times our volume that we just found. 4100 39 19.3 finds 4003 d night. Did you get each 0.0 eight times? 10 to the fourth craps. I notice my sig figs are once again three sig figs because we have 366 and our initial number. Okay, Now, look, let's look at part B to give you a cube of platinum of edge like 0.40 millimeters and density planet was 21.4 grounds for centimeter execute. So one thing you should notice right off the bat is that the units are different, right? I have the edge length in millimeters, but the density of platinum has a centimeters cute value. So we have to change the, um, platinum of the plan of edge length two centimeters first. So, um, let's just do that real quick. Do a quick incursion. Syria 0.40 millimeters times one centimeter and then how many millimeters on one centimeter? You have 10 right? 10 millimeters. No. One centimeter. How The number of years will cancel out very nicely and we'll have 2.4 zero centimeters. Okay, now we can just find our volume before you for a hue is what are square are cute. Great. Because, um, the sidelines, they're all the same. So zero point 00 for zero centimeters to the third power 0.407 years to the third power. And you should get 6.4 times 10 Teoh. Negative. Eight centimeters. Cute. Ok, now we can just plug the street into our mass equation. Um, and we can have eso. What's the density? They give us 21.4 grams percent of your execute again, the units will cancel lottery. And I sleep here times 6.4 times 10 to the negative. Eight centimeters cube, which is the volume we just found. Centimeters Cube will cancel out. And then, um, split was in your calculator. Eight. And then you get one point for times 10 to the negative six grabs. Okay. Pretty simple. And this one is only two sig figs because our initial value only has 26 fix right now. See, um, see, is actually quite a bit more simple than the other ones. Basically, they give it to you. They give you the volume straight up, so you can just multiply it by the density. Um, so mass. Now notice that it's a different type of volume that we were working with before I'm even working with Sammy was cued, right? But this is male leaders, so it just shows that any type of volume can work with the density as long as the density and the volume are in the same units. Okay, so they give you 50 milliliters of methanol. Times zero point 79 eight grabs per millimeter. Actually, these are exactly the same. Announced volume. Said he was cute and a mill leader. Exactly the same volume. Just been written in a different way. So plug a student to your calculator. You should get 39 29 Gramps and three Sig figs because our initial value waas 50.366 That's basically it for this question. Pretty simple, but very important. Density is very important chemistry and just science in general. So I hope this is helpful. And thank you for listening.

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