Martinchristopherdavidn
Answered

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Sulfur hexafluoride is a colorless, ordorless, very unreactive gas. Calculate the pressure (in atm) exerted by 187 grams of the gas in a steel vessel of volume 4.50 L at 79.5°C.​

Sagot :

SOLUTION:

Step 1: List the given values.

[tex]\begin{aligned} & V = \text{4.50 L} \\ & mass = \text{187 g} \\ & T = 79.5^{\circ}\text{C} = \text{352.65 K} \end{aligned}[/tex]

Step 2: Calculate the molar mass of the gas (SF₆).

The molar masses of S and F are 32.06 g/mol and 18.998 g/mol, respectively.

[tex]\begin{aligned} MM & = \text{32.06 g/mol + 6(18.998 g/mol)} \\ & = \text{146.05 g/mol} \end{aligned}[/tex]

Step 3: Calculate the number of moles of the gas.

[tex]\begin{aligned} n & = \frac{mass}{MM} \\ & = \frac{\text{187 g}}{\text{146.05 g/mol}} \\ & = \text{1.2804 mol} \end{aligned}[/tex]

Step 4: Solve for the pressure of the gas by using ideal gas equation.

[tex]\begin{aligned} P & = \frac{nRT}{V} \\ & = \frac{(\text{1.2804 mol})\left(0.082057 \: \dfrac{\text{L}\cdot\text{atm}}{\text{mol}\cdot\text{K}}\right)(\text{352.65 K})}{\text{4.50 L}} \\ & = \boxed{\text{8.23 atm}} \end{aligned}[/tex]

Hence, the pressure exerted is 8.23 atm.

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