Question

What volume of H2 gas (in L), at 748 mmHg and 86 °C, is required to synthesize 25.8 g CH3OH ? How many liters of CO gas, measured under the same conditions, are required?

Answer 1

Answer: Thus volume of hydrogen is 48.7 L and volume of CO is 24.4 L

Step-by-step explanation:

The balanced chemical reaction is :

`CO+2H_2\rightarrow CH_3OH`

To calculate the moles :

`\text{Moles }=\frac{\text{given mass}}*{\text{Molar Mass}}`

`\text{Moles of} CH_3OH=(25.8g)/(32g/mol)=0.81moles`

According to stoichiometry :

1 mole of
`CH_3OH` require = 2 moles of
`H_2`

Thus 0.81 moles of
`CH_3OH` will require=
`(2)/(1)* 0.81=1.62moles` of
`H_2`

To find Volume of hydrogen :

According to ideal gas equation :

`PV=nRT`

P= pressure of gas = 748 mm Hg = 0.98 atm (760mmHg=1atm)

R = Gas constant =
`0.0821\text{ L atm }mol^(-1)K^(-1)`

T = temperature of the gas =
`86^0C=(273+86)K=359K`

V = volume of gas = ?

n = number of moles = 1.62

`0.98* V=1.62* 0.0821* 359`

`V=48.7L`

According to stoichiometry :

2 moles of
`H_2` require = 1 moles of
`CH_3OH`

Thus 1.62 moles of
`H_2` will require=
`(1)/(2)* 1.62=0.81moles` of
`CO`

To find Volume of CO:

`0.98* V=0.81* 0.0821* 359`

`V=24.4L`

Thus volume of hydrogen is 48.7 L and volume of CO is 24.4 L