Question

Considering that the mantle is 44.8% oxygen and 21.5% silicon by mass, calculate the mole ratio of oxygen atoms to silicon atoms in the mantle.

Answer 1

Answer: The mole ratio of oxygen atoms to silicon atoms in mantle is 3.6 : 1

Step-by-step explanation:

To calculate the mole ratio of oxygen and silicon in mantle, use will follow some steps:

Step 1: Converting Mass percent into mass of Oxygen and Silicon.

We are given 44.8% of oxygen is present in mantle by mass.

This means that 44.8 grams of oxygen is present in 100 grams of mantle.

Similarly, 21.5 grams of silicon is present in 100 grams of mantle.

Step 2: Calculating the moles of Oxygen and Silicon.

To calculate the number of Moles, we will use the formula:

`Moles=\frac{\text{Giver mass}}{\text{Molar Mass}}`

• For Oxygen:

Molar mass of oxygen = 16 g/mol

Given mass of oxygen = 44.8 grams

Putting values in above equation, we get:

`Moles=(44.8g)/(16g/mol)\\\\\text{Moles of oxygen}=2.8moles`

• For Silicon:

Molar mass of silicon = 28 g/mol

Given mass of silicon = 21.5 grams

Putting values in above equation, we get:

`Moles=(21.5g)/(28g/mol)\\\\\text{Moles of silicon}=0.767moles`

Step 3: Calculating the number of atoms of Oxygen and Silicon.

According to mole concept:

1 mole of an element contains
`6.022* 10^(23)` number of atoms.

• Calculating the number of atoms of Oxygen:

2.8 moles of oxygen will contain
`2.8* 6.022* 10^(23)=16.8816* 10^(23)` atoms

• Calculating the number of atoms of Silicon:

0.767 moles of silicon will contain
`0.767* 6.022* 10^(23)=4.618* 10^(23)` atoms

Step 4: Calculating the mole ratio of Oxygen and Silicon atoms

Mole ratio of atoms of Oxygen : Silicon =
`16.8816* 10^(23):4.618* 10^(23)=3.6:1`

Hence, the mole ratio of atoms of Oxygen and Silicon is 3.6 : 1

Answer 2

The mantle has a mass of around
`4.278 X 10 ^2^4 kg` that is around 68.4% of earth's mass.

So to calculate moles we need to first find out the mass of oxygen and silicon present in mantle. It is given that oxygen is 44.8% by mass in mantle and 21.5% by mass in mantle, therefore to calculate its mass, we need to use
`\text{mass percentage }=\frac{\text{mole of solute}}{\text{mass of solution}}*100`

Now, to calculate mass percentage of oxygen

`44.8 =(x)/(4.278X10^2^4kg)*100`

`x= 191.65*10^2^2kg`

Similarly the mass of silicon can be calculated

`21.5 =(x)/(4.278X10^2^4kg)*100`

`x=91.977*10^2^2kg`

Now, the moles of any substance is calculated by

`\text{moles}= \frac{\text{given mass}}{\text{molar mass}}`

`\text{moles of oxygen}= (191.65*10^2^2kg)/(2.6566962*10^-^2^6kg)`

where, mass of oxygen in kilograms is
`2.6566962*10^-^2^6kg`

So,
`\text{moles of oxygen}=72.1384*10^4^8\text{moles of O}`

Similarly
`\text{moles of silicon}= (91.977*10^2^2kg)/(4.663*10^-^2^6kg)`

`\text{moles of silicon}=19.724*10^4^8\text{moles of Si}`

Now, to calculate mole ratio we need to divide every moles to the lowest calculated mole that is the moles of Si and round it off to the nearest whole number.

`\text{mole ratio of oxygen}= (72.138*10^4^8kg)/(19.724*10^4^8kg)`

`=3.65\approx 4`

`\text{mole ratio of Silicon}=(19.724*10^4^8)/(19.724*10^4^8)`

`=1`

`\text{Mole ratio of Oxygen : Mole ratio of Silicon} = 4:1`