Answered

Acetylene gas ([tex]\(C_2H_2\)[/tex]) reacts with oxygen gas ([tex]\(O_2\)[/tex]) to produce carbon dioxide ([tex]\(CO_2\)[/tex]) and water vapor ([tex]\(H_2O\)[/tex]) at STP.

How many liters of [tex]\(C_2H_2\)[/tex] are required to produce 75.0 L of [tex]\(CO_2\)[/tex]?

[tex]\[\square\][/tex] L



Answer :

To determine the volume of acetylene gas [tex]\((C_2H_2)\)[/tex] required to produce 75.0 liters of carbon dioxide [tex]\((CO_2)\)[/tex] at standard temperature and pressure (STP), we will use the balanced chemical equation for the reaction between [tex]\(C_2H_2\)[/tex] and [tex]\(O_2\)[/tex]:

[tex]\[ 2 \, C_2H_2 + 5 \, O_2 \rightarrow 4 \, CO_2 + 2 \, H_2O \][/tex]

From the balanced equation, we can observe the following stoichiometric relationship between [tex]\(C_2H_2\)[/tex] and [tex]\(CO_2\)[/tex]:

- 2 volumes of [tex]\(C_2H_2\)[/tex] produce 4 volumes of [tex]\(CO_2\)[/tex].

This can be simplified to show that:

- 1 volume of [tex]\(C_2H_2\)[/tex] produces 2 volumes of [tex]\(CO_2\)[/tex].

With this relationship in mind, we can set up the following ratio to find the volume of [tex]\(C_2H_2\)[/tex] needed to produce the desired volume of [tex]\(CO_2\)[/tex]:

[tex]\[ \frac{1 \, \text{volume of} \, C_2H_2}{2 \, \text{volumes of} \, CO_2} = \frac{X \, \text{liters of} \, C_2H_2}{75.0 \, \text{liters of} \, CO_2} \][/tex]

Solving for [tex]\(X\)[/tex], we get:

[tex]\[ X = \frac{75.0 \, \text{liters of} \, CO_2}{2} \][/tex]
[tex]\[ X = 37.5 \, \text{liters of} \, C_2H_2 \][/tex]

Therefore, the volume of [tex]\(C_2H_2\)[/tex] required to produce 75.0 liters of [tex]\(CO_2\)[/tex] at STP is:

[tex]\[ \boxed{37.5} \, \text{liters} \][/tex]