Question

In a year an adult cow produces around 3.571 x 10^27 molecules of methane CH4 a greenhouse gas how many moles of methane does this cow produce in a year

Answer 1

`\boxed{\boxed {\sf 5930.0 \ mol \ CH_4}}`

Step-by-step explanation:

We are asked to find how many moles of methane (CH₄) a cow produces in a year. We must convert molecules of methane to moles of methane. We will do this using Avogadro's Number or 6.022 × 10²³. This is the number of particles (atoms, molecules, formula units, etc.) in 1 mole of a substance.

In this case, the particles are molecules of methane. There are 6.022 × 10²³ molecules of methane in 1 mole.

We will convert molecules to moles using dimensional analysis. Set up a ratio using Avogadro's Number.

`\frac {6.022 * 10^(23) \ molecules \ CH_4}{ 1 \ mol \ CH_4}`

We are converting 3.571 × 10²⁷ molecules of methane to moles, so we multiply the ratio by this value.

`3.571 * 10^ {27} \ molecules \ CH_4 *\frac {6.022 * 10^(23) \ molecules \ CH_4}{ 1 \ mol \ CH_4}`

Flip the ratio. It is still the same value, but the units of molecules of methane cancel.

`3.571 * 10^ {27} \ molecules \ CH_4 *\frac { 1 \ mol \ CH_4}{6.022 * 10^(23) \ molecules \ CH_4}`

`3.571 * 10^ {27} *\frac { 1 \ mol \ CH_4}{6.022 * 10^(23) }`

`\frac {3.571 * 10^ {27}}{6.022 * 10^(23) } \ mol \ CH_4`

`5929.923613 \ mol \ CH_4`

The original measurement of molecules of methane( 3.571 × 10²⁷ molecules) has 4 significant figures, so our answer must have the same. For the number we calculated, that is the ones place. The 9 in the tenth place tells us to round the 9 in the ones place up to a 0, then the 2 in the tens place up to a 3.

`5930 \ mol \ CH_4`

We must add a placeholder zero in the tenth place to reach 4 sig figs.

`5930.0 \ mol \ CH_4`

The adult cow produces approximately 5930.0 moles of methane in a year.