Question

For the reaction H2(g) +O2(g) — H2O (g) how many liters of water can be made from 5 L of oxygen gas at 37.0 Celsius, 1.76atm and an excess of hydrogen?

Answer 1

12.5 L

Step-by-step explanation:

Part 1 - Finding Number of moles

First thing we need to find out is number of moles of oxygen gas. We can achieve this using the formula: PV=nRT

Pressure (Pa) x Volume (cubic meters) = no. moles x gas constant (8.31 J/K*mol) x Temperature (K)

We can rearrange this formula to solve for no. moles:
`n=(PV)/(RT)` and plug in the values to solve.

1 atm = 1.01325 x 10^5 Pa, therefore 1.76atm =
`1.76*1.01325*10^(5) =178332Pa`

1 L = 1 x 10^-3 m^3, therefore 5L =
`5*1*10^(-3)=5*10^(-3)m^(3)`

Finally Kelvin = Celsius + 273.15, therefore 37.0C =
`37.0+273.15=310.15K`

Substituting this all back into the formula we get:

`n=((178332)(5*10^(-3)))/((8.31)(310.15))`

`n=(891.66)/(2577.3465)`

`n=0.346` moles (3.s.f)

Part 2 - Balancing Equation

The equation given is not balanced so we need to balance it to find the correct molar ratio. We can start by balancing the oxygens as there are less of them. We can see that there are 2 oxygen atoms on the left as denoted by 'O2' but only one on the right in 'H2O', therefore we can add a two in front of the H2O on the right side to balance the oxygen atoms:

`H_(2(g)) +O_(2(g)) - > 2H_(2) O_((g))`

Now we have four hydrogens on the right side so we have a 2 in front of H2 on the left hand side to balance the hydrogens:

`2H_(2(g)) +O_(2(g)) - > 2H_(2) O_((g))`

And voila! The equation is balanced and shows the correct molar ratio.

Part 3 - Calculating moles of water

As we can see from the molar ratio in the balanced equation, every mole of O2 will produce two moles of H2O- the ratio is 1:2. As we have an excess of hydrogen, we only need to worry about the amount of oxygen we have. Therefore to calculate the number of moles of water that can be made we simply need to multiple by the ratio:

`0.346*2=0.692` moles of water

Part 4 - Converting to Liters

Finally, to convert our amount of moles into volume, we can use water's molecular mass to find the mass and then its density to find its volume. Water's molecular mass is 18.02gmol^-1 (2x1.01+16.00) and its density is 997kg/m^3.

m=nM (mass = no. moles x molecular mass): m=
`0.692*18.02=12.46984g`

rho = m/v (density = mass/volume):
`997=12.46984/v`, therefore
`v=0.0125m^(3)`

Finally as mentioned above, 1 L = 1 x 10^-3 m^3, therefore the volume of water that can be made is 12.5 Liters.