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tresset_1 [31]
3 years ago
5

In the reaction below, if 5.71 g of sulfur is reacted with 10.0 g of oxygen, how many grams of sulfur trioxide will be produced?

Chemistry
1 answer:
yawa3891 [41]3 years ago
3 0

Answer:

14.3 g SO₃

Explanation:

2S + 3O₂ → 2SO₃

First, find the limiting reactant.  To do that, calculate the mass of oxygen needed to react with all the sulfur.

5.71 g S × (1 mol S / 32 g S) = 0.178 mol S

0.178 mol S × (3 mol O₂ / 2 mol S) = 0.268 mol O₂

0.268 mol O₂ × (32 g O₂ / mol O₂) = 8.57 g O₂

There are 10.0 g of O₂, so there's enough oxygen.  The limiting reactant is therefore sulfur.

Use the mass of sulfur to calculate the mass of sulfur trioxide.

5.71 g S × (1 mol S / 32 g S) = 0.178 mol S

0.178 mol S × (2 mol SO₃ / 2 mol S) = 0.178 mol SO₃

0.178 mol SO₃ × (80 g SO₃ / mol SO₃) = 14.3 g SO₃

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The question is incomplete, here is the complete question:

Sulfuric acid is essential to dozens of important industries from steel making to plastics and pharmaceuticals. More sulfuric acid is made than any other industrial chemical, and world production exceeds  2.0×10¹¹ kg per year.

The first step in the synthesis of sulfuric acid is usually burning solid sulfur to make sulfur dioxide gas. Suppose an engineer studying this reaction introduces 1.8 kg of solid sulfur and 10.0 atm of oxygen gas at 650°C  into an evacuated 50.0 L tank. The engineer believes Kp = 0.099 for the reaction at this temperature.

Calculate the mass of solid sulfur he expects to be consumed when the reaction reaches equilibrium. Round your answer to 2 significant digits.

<u>Answer:</u> The mass of solid sulfur that will be consumed is 19. grams

<u>Explanation:</u>

The chemical equation for the formation of sulfur dioxide gas follows:

                    S(s)+O_2\rightarrow SO_2(g)

<u>Initial:</u>                   10.0

<u>At eqllm:</u>              10-x         x

The expression of K_p for above equation follows:

K_p=\frac{p_{SO_2}}{p_{O_2}}

We are given:

K_p=0.099

Putting values in above expression, we get:

0.099=\frac{x}{10-x}\\\\x=0.901atm

Partial pressure of sulfur dioxide = x = 0.901 atm

To calculate the number of moles, we use the equation given by ideal gas which follows:

PV=nRT

where,

P = pressure of the sulfur dioxide gas = 0.901 atm

V = Volume of the gas = 50.0 L

T = Temperature of the gas = 650^oC=[650+273]K=923K

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

n = number of moles of sulfur dioxide gas = ?

Putting values in above equation, we get:

0.901atm\times 50.0L=n\times 0.0821\text{ L. atm}mol^{-1}K^{-1}\times 923K\\\\n=\frac{0.901\times 50.0}{0.0821\times 923}=0.594mol

By stoichiometry of the reaction:

1 mole of sulfur dioxide gas is produced from 1 mole of sulfur

So, 0.594 moles of sulfur dioxide gas will be produced from = \frac{1}{1}\times 0.594=0.594mol of sulfur

  • To calculate the number of moles, we use the equation:

\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}

Moles of sulfur = 0.594 moles

Molar mass of sulfur = 32 g/mol

Putting values in above equation, we get:

0.594mol=\frac{\text{Mass of sulfur}}{32g/mol}\\\\\text{Mass of sulfur}=(0.594mol\times 32g/mol)=19.008g

Hence, the mass of solid sulfur that will be consumed is 19. grams

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