Question regarding Chemistry ( Moles

[SiriusA]

Homework Statement

A silicon chip used in an integrated circuit of a computer has a mass of 4.86 mg. How many silicon atoms are present in this chip?

Homework Equations

no. of moles of element = no. of particles / 6.22 * 10^23 particles


No. of moles of a element : mass of element in g / molar mass of element in g/mol

3. Attempt at solution

No. of moles in element = 4.86 / 28 = 0.1736 mol

no. of moles = 0.1736 * 6.22 * 10^23 particles
= 1.079792e23 particles
Just want to make sure if the answer is correct .


And another question :

If 200.0 mL of 10.0 ºC water and 250.0 mL of 40.0 ºC water are added together, what will be the final temperature of the mixed water? (Assume no heat is transferred to or from the surroundings.)

We know that: Change in energy of the water = mass * specific heat * change in temp .
therefore the energy amount going out of the warm water is equal to the energy amount going into the cool water.

Cold Water Hot Water
mass * specific heat * change in temp. = mass * specific heat * change in temp.

200 * 4.184 * (40 - x ) = 250 * 4.184 * (x - 10 )

836.8 *( 40 - x ) = 1046 * (x - 10)

33472 - 836.8x = 1046x - 10460

1882.8x = 43932

x = 23.3 degrees but the answer is wrong :C Please help urgently !

 

[happysmiles36]

Lay out everything you have given and need (in the right units!<-- if you take physics you will understand).

You start out with mg (milligrams NOT grams)
Mass: 4.86mg x 1g / 1000mg = 0.00486g
6.22x10^23 atoms/mol <----- (I think this is supposed to be 6.02x10^23 atoms/mol because that is avogadro's number. If you get the wrong answer just change it because I don't know what your teacher told you.)
Molar Mass: 28.09g/mol

You want moles so:

Mole/Mass x Mass = Mole
^ Molar Mass

Mole x 6.22x10^23 atoms/mol = ### of atoms.

Three significant digits.
----------------------------
Questions 2:

One thing to know is you can cancel stuff before you do all the math (in this case you don't even need a calculator!)

so

(200)(x-10)(4.184)=(250)(40-x)(4.184)
The specific heat of water is the same on both sides so they cancel.
You end up with:
(200)(x-10)=(250)(40-x)
Rest should be simple.
x is final temp.


TO SUM IT UP:
Your mistake in Q1: Wrong units, wrong particles/mol (Not correct # for avogadro's number) <-- I am pretty sure of this
Your mistake in Q2: You have 200ml with the 40 °C temperature and the 250ml with the 10°C temperature so your answer will be lower than the correct answer (you have more of a lower temp water)


GL