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Acetylene torches are used for welding. These torches use a mixture of acetylene gas, C2H2, and oxygen gas, O2 to produce the following combustion reaction: 2C2H2(g)+5O2(g)→4CO2(g)+2H2O(g) Imagine that you have a 6.50 L gas tank and a 4.00 L gas tank. You need to fill one tank with oxygen and the other with acetylene to use in conjunction with your welding torch. If you fill the larger tank with oxygen to a pressure of 115 atm , to what pressure should you fill the acetylene tank to ensure that you run out of each gas at the same time? Assume ideal behavior for all gases.

Respuesta :

Answer:

Pressure in acetylene gas tank will be 74.8atm

Explanation:

Step 1: Using the ideal gas equation, determine the number of moles of oxygen

[tex]n=\frac{PV}{RT}[/tex]

[tex]P_O=115atm[/tex]

[tex]V_O=6.50L[/tex]

[tex]n_O=\frac{P_OV_O}{RT}[/tex]

[tex]n_O=\frac{115*6.50}{RT}[/tex]

[tex]n_O=\frac{747.5}{RT}[/tex]

As temperature is unknown and assumed to be the same for both gases, and the ideal gas constant will be the same for both cases, these values are left as constants 'T' and 'R'.

Step 2: Determine the proportionate number of moles of acetylene required based on the chemical equation

2 moles of acetylene require 5 moles of oxygen for complete combustion

Thus, 0.4 moles of acetylene are required per mole of oxygen

[tex]n_A=0.4n_O[/tex]

[tex]n_A=0.4*\frac{747.5}{RT}[/tex]

[tex]n_A=\frac{299}{RT}[/tex]

Step 3: Determine the pressure of acetylene tank required in 4.00L tank

[tex]n_A=\frac{P_AV_A}{RT}[/tex]

[tex]\frac{299}{RT}=\frac{P_A*4.00}{RT}[/tex]

[tex]P_A=\frac{299}{4.00}[/tex]

[tex]P_A=74.75 atm[/tex]

Assumptions:

Temperature is the same for both gases and constant

The ideal gas constant is the same for both gases

The combustion reaction is complete and there are no limiting factors

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