Question

Carbon monoxide gas reacts with hydrogen gas to form methanol.CO(g)+2H2(g)?CH3OH(g)A 1.30L reaction vessel, initially at 305 K, contains carbon monoxide gas at a partial pressure of 232 mmHg and hydrogen gas at a partial pressure of 387mmHg .Identify the limiting reactant and determine the theoretical yield of methanol in grams.

Answer 1

Answer : The limiting reagent is hydrogen gas and the theoretical yield of
`CH_3OH` is 0.422 grams.

Explanation :

First we have to calculate the moles of
`CO_2` and
`H_2` gas.

Using ideal gas equation :

`PV=nRT\\\\n_(CO_2)=(P_(CO_2)V)/(RT)`

where,

P = partial pressure of
`CO_2` gas = 232 mmHg = 0.305 atm

conversion used : (1 atm = 760 mmHg)

V = Volume of gas = 1.30 L

n = number of moles
`CO_2` gas = ?

R = Gas constant =
`0.0821L.atm/mol.K`

T = Temperature of gas = 305 K

Putting values in above equation, we get:

`n_(CO_2)=((0.305atm)* (1.30L))/((0.0821L.atm/mol.K)* (305K))`

`n_(CO_2)=0.0158mole`

and,

P = partial pressure of
`H_2` gas = 387 mmHg = 0.509 atm

`n_(H_2)=((0.509atm)* (1.30L))/((0.0821L.atm/mol.K)* (305K))`

`n_(H_2)=0.0264mole`

Now we have to calculate the limiting and excess reagent.

The balanced chemical reaction is,

`CO(g)+2H_2(g)\rightarrow CH_3OH(g)`

From the balanced reaction we conclude that

As, 2 mole of
`H_2` react with 1 mole of
`CO`

So, 0.0264 moles of
`H_2` react with
`(0.0264)/(2)=0.0132` moles of
`CO`

From this we conclude that,
`CO` is an excess reagent because the given moles are greater than the required moles and
`H_2` is a limiting reagent and it limits the formation of product.

Now we have to calculate the moles of
`CH_3OH`

From the reaction, we conclude that

As, 1 mole of
`H_2` react to give 2 mole of
`CH_3OH`

So, 0.0264 moles of
`H_2` react to give
`(0.0264)/(2)=0.0132` moles of
`CH_3OH`

Now we have to calculate the mass of
`CH_3OH`

`\text{ Mass of }CH_3OH=\text{ Moles of }CH_3OH* \text{ Molar mass of }CH_3OH`

Molar mass of methanol = 32 g/mole

`\text{ Mass of }CH_3OH=(0.0132moles)* (32g/mole)=0.422g`

Therefore, the theoretical yield of
`CH_3OH` is 0.422 grams.