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What is the mass of 6.299 × 1023 atoms C? Answer in units of g

What is the mass of 6.299 × 1023 atoms C? Answer in units of g

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If you meant 10 to the power 23 then the answer is 12g as this is the number of particles in one mole of carbon
jgopee
29 November 2012
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Masses and Moles

Take a look at your laptop or smartphone closely, ever thought about what it is made up of? Of course, it has electronic components in it but what are these electronic components made up of? What happens if we take a look at these substances at the atomic level? You will be looking at atoms. Atoms are the building blocks of all the substances in this world but the question is, how do we measure atoms? The simplest answer is with moles. So, how do we calculate moles of any element or compound? Keep on reading.

How To Calculate Mass and Moles of an Element?

Every object that occupies space has mass. Mass is a universal quantity that represents the total amount of matter in an object. Mass and weight might look the same but they are different, therefore, do not get confused between terms. Mass will remain constant, no matter where you are. The mass of an element is the average mass of the atoms present in an element. It is measured in the atomic mass unit (amu). If you want to find the mass of an individual element (that contains 1 mole), you can check it out from the periodic table. Don't get confused with that amount of information, to find the mass of an element, all you need to check is the atomic weight. For example, let's pick hydrogen, the first element of the periodic table. It is written in this form:

{ 1 }^{ H }_{ 1.0078 }

The letter "H" represents the element, which is the hydrogen in the above case. The number above the letter "H" represents the atomic number and the number below the letter "H" represents the atomic mass. We are interested in atomic mass only for now and that is the mass of an element having one mole. Does that mean that every number below their element represents atomic mass? Yes but don't forget that the atomic mass shown in the periodic table is calculated under the basis of one mole. If the mole is not equal to one then you need to calculate the mass of the element from a different method.

Calculation of Mass Using Moles

Speaking about calculating the mass for an element whose mole is not equal to one, there are several ways to calculate the mass of an element. For example, you are asked to find the mass of calcium that has 2 moles. How to find the mass of an element with a varying mole number? With the help of this formula:

Mass = Moles x Atomic mass

The atomic mass of calcium is around 40 and the question provided 2 moles of calcium.

Mass = 2 x 40

Mass = 80 amu

Let's do one more question and then head for the next section. Suppose you are asked to find the mass of sulfur having 0.2 moles.

Mass = Moles x Atomic mass

The atomic mass of sulfur is around 32 and the question provided 0.2 moles of calcium.

Mass = 0.2 x 32

Mass = 6.4 amu

Calculation of Mass and Moles Using Avogadro's Constant

One mole of any element or compound contains 6.02 x 10 23 particles. This is known as the Avogadro's number. This constant was found by an Italian scientist whose name is Amedeo Avogadro. Basically, this constant is a ratio of the number of particles in an object and the amount of substance in an object. Therefore, all elements in the periodic table contain 6.02 x 10 23 particles. Don't forget that one mole is equal to 6.02 x 10 23 particles.  Suppose you are given a question to find the mass of carbon which has 3.01 x 10 23 particles. To find the mass and moles using the number of particles, you need to use the below equation:

Moles = Number of particles / Avogadro's constant

  From this formula, you will find the moles and then use the above method to find the mass of carbon.

Step 1: Find the number of moles

Moles = Number of particles / Avogadro's constant Moles = 3.01 x 10 23 / 6.02 x 10 23 = 0.5

Step 2: Find the mass using the moles

Mass = Moles x Atomic mass C = 12 amu          Moles = 0.5 Mass = 0.5 x 12 = 6 amu

Calculation of Mass and Moles Using Volume

There is a small trick of calculating mass using volume. The main parameters of volume are pressure and temperature. With changes in any of the parameters will result in a change in volume. Therefore, scientists came up with standards. Currently, there are three common standards and they are:

  • RTP (Room Temperature and Pressure)
  • STP (Standard Temperature and Pressure)
  • NTP (Normal Temperature and Pressure)

One mole of gas occupies 24 dm3 volume at RTP conditions. However, one mole of gas occupies 22.4 dm3 volume at STP and NTP conditions. Therefore, do check which conditions you are working in. To find the mass of an element or compound using the volume data, you will be needing this formula:  

Moles = Volume occupied / 24 dm3     (For RTP case)

Moles = Volume occupied / 22.4 dm3     (For STP & NTP case)

Here is an example involving volume, find the mass of sodium that occupies 6 litres at room temperature and pressure. Again, we will have two steps to solve this problem.

Step 1: Find the number of moles

Moles = Volume occupied / 24 dm3 1 L = 1 dm3 , therefore, 6 L = 6 dm3 Moles = 6 / 24 = 0.25

Step 2: Find the mass using the moles

Mass = Moles x Atomic mass Na = 23 amu      Moles = 0.25 Mass = 0.25 x 23 = 5.75 amu

Calculation of Mass and Moles Using Concentration

Often times you will be provided with the concentration of any solution and you will be asked to find the moles and mass of the solution. As usual, you will be needing a formula and this is how you find the moles of the solution:

Moles = Concentration x Volume

Don't forget the volumetric condition provided. Once you found the moles, you can easily find the mass of the solution using the general mole equation relating original mass and mass provided. For example, you have a solution of bromine at 4.3 mol.dm-3 and the volume of the solution is 10 dm3 at NTP. Find the moles and mass of bromine.

Step 1: Find the number of moles

Moles = Conc. x volume Moles = 4.3 x 10 Moles = 43

Step 2: Find the mass using the moles

Mass = Moles x Atomic mass Br = 80     Moles = 43 Mass = 43 x 80 = 3440 amu Did you notice something? In the above question, the NTP doesn't matter because we were already provided with the volume. The purpose of this question is to trick you into whether you use the provided volume or use the standard volume at NTP. Always use the volume provided in the formula and if not provided then go with the standard volume! Here is another question that uses the volumetric condition. Find the number of moles and mass of the mercury having the concentration of 0.12 mol.dm-3 at STP.

Step 1: Find the number of moles

Moles = Conc. x volume Moles = 0.12 x 22.4 Moles = 2.688

Step 2: Find the mass using the moles

Mass = Moles x Atomic mass Hg = 200     Moles = 2.688 Mass = 2.688 x 200 = 537.6 amu

What is the Difference between Mass and Moles?

At this point, you have a good idea of what is a mole and the mass of an element but you might be thinking what is the difference between mass and moles? To be fair, they both represent the same quantity which is the total matter occupied by an element. Whenever we talk about the mass of an element, we usually mean the molecular mass/atomic mass of an element on the basis of 1 mole. Atomic mass is the total matter in an element. This mass is calculated relative to the Carbon-12 atom. It means that atomic mass is expressed as multiple of 1/12 the mass of Carbon-12 and that is where its unit becomes amu (where 1 amu = 1.660539040 x 10-24 grams). If you check the periodic table, almost all elements don't have fixed masses. This is because almost all element's isotopes are available on Earth. Based on their isotope percent, they are mentioned in the periodic table. For example, check carbon, you will see the mass of 12.009. There are two types of carbon available on Earth, Carbon-12, and Carbon-13 (which is an isotope of Carbon-12). If all isotopes were added to the periodic table, it would be a big trouble to understand and more likely for errors. That is why chemists came up with the idea of calculating the average atomic mass of every element according to their abundance on Earth. Let's talk about our Carbon atomic mass problem again. The abundance of Carbon-12 is about 98.89% and Carbon-13 is about 1.11%.  

Why Do We Calculate Moles Instead of Using Atomic Mass?

A Mole represents 6.02 x 1023  particles in an element. Working with such a big unit can lead to many problems and errors. To make it easy to work with, chemists came up with the mole idea. They suggested equating such big numbers to easy numbers for very small entities. Today, the concept of moles helps a lot in the chemistry domain and it also reduces the probability of calculation error. For example, now you know that every element has a different atomic mass. Working with their standard mass (it means the total matter they occupy for 6.02 x 1023 particles) could give a hard time for many chemists. Most of the time will be wasted on proof-checking their work rather than focusing on the next work. Instead, they use the mole's concept to make their work easier and it doesn't need a lot of time in proof-checking.