How many molecules are in 0.454 kg of carbon dioxide?

Question

Jeremiah Adams · Accepted Answer

How many molecules in a pound of carbon dioxide?

#(454*g)/(44.0*g*mol^-1)xxN_A#, where #N_A=6.022xx10^23*mol^-1#.

#N_A# #=# #"Avogadro's number"# #=# #6.022xx10^23*mol^-1#. By definition, in #44.0*g# of carbon dioxide there are #"Avogadro's number"# of carbon atoms, and #2xx"Avogadro's number"# of oxygen atoms. Therefore, we just compute the product: #(454*g)/(44.0*g*mol^-1)xxN_A# #~=# #10N_A#

Caleb Adams · Answer

undefined In 0.454 kg, there are roughly 1.82 x 10^25 molecules of carbon dioxide.

HIX Tutor · Answer

undefined Great question! Let's figure it out together.

1. **Know the formula for carbon dioxide (CO₂)**: It has one carbon atom and two oxygen atoms.

2. **Find the molar mass of CO₂**:
   - Carbon (C) = 12 g/mol 
   - Oxygen (O) = 16 g/mol 
   - CO₂ = 12 + (2 × 16) = 12 + 32 = 44 g/mol

3. **Convert 0.454 kg to grams**:
   - 0.454 kg = 454 grams (1 kg = 1000 grams).

4. **Calculate how many moles are in 454 grams**:
   - Moles = mass (g) / molar mass (g/mol)
   - Moles of CO₂ = 454 g / 44 g/mol ≈ 10.36 moles.

5. **Find the number of molecules**:
   - Use Avogadro's number, which is about 6.02 x 10²³ molecules/mole.
   - Number of molecules = moles × Avogadro's number.
   - ≈ 10.36 moles × 6.02 x 10²³ molecules/mole.

6. **Calculate the final number**:
   - ≈ 6.23 x 10²⁴ molecules.

So, how does that sound? Do you see how we figured it out step by step?