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What volume would 74.87g of CO2 occupy at STP

Sagot :

Sarah06109

Answer:

[tex]\boxed {\boxed {\sf 38.11 \ L}}[/tex]

Explanation:

To find the volume, we need to convert grams to moles, then moles to liters.

1. Convert Grams to Moles

We convert grams to moles using the molar mass. This is the mass of 1 mole of a substance. It is the same as the atomic mass found on the Periodic Table, but the units are grams per mole (not atomic mass units).

We have the compound carbon dioxide or CO₂. Look up the molar masses of the individual elements.

  • C: 12.011 g/mol
  • O: 15.999 g/mol

Notice that oxygen has a subscript of 2, so there are 2 atoms in each molecule. We have to multiply oxygen's molar mass by 2 before adding carbon's.

  • O₂: 15.999 *2=31.998 g/mol
  • CO₂: 12.011 + 31.998=44.009 g/mol

Use this value as a ratio.

[tex]\frac {44.009 \ g\ CO_2}{1 \ mol \ CO_2}[/tex]

Multiply by the given number of grams: 74.87

[tex]74.87 \ g\ CO_2*\frac {44.009 \ g\ CO_2}{1 \ mol \ CO_2}[/tex]

Flip the ratio so the units of grams cancel.

[tex]74.87 \ g\ CO_2*\frac {1 \ mol \ CO_2}{44.009 \ g\ CO_2}[/tex]

[tex]74.87 *\frac {1 \ mol \ CO_2}{44.009 }[/tex]

[tex]{74.87 \ mol \ CO_2}{44.009 } = 1.701242928 \ mol \ CO_2[/tex]

2. Convert Moles to Liters

Any gas at standard temperature and pressure (STP) has a volume of 22.4 liters per mole.

[tex]\frac {22.4 \ L}{1 \ mol \ CO_2}[/tex]

Multiply by the number of moles we calculated.

[tex]1.701242928 \ mol \ CO_2*\frac {22.4 \ L}{1 \ mol \ CO_2}[/tex]

The units of moles cancel.

[tex]1.701242928 *\frac {22.4 \ L}{1 }[/tex]

[tex]1.701242928 *{22.4 \ L}= 38.10784158 \ L[/tex]

3. Round

The original measurement has 4 significant figures, so our answer must have the same. For the number we calculated, that is the hundredth place.

  • 38.10784158

The 7 tells us to round the 0 10 a 1.

[tex]38.11 \ L[/tex]

74.87 grams of carbon dioxide occupies a volume of approximately 38.11 liters.

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