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The volume occupied by 4.75 g of acetylene gas at 50°C and 740 mm Hg pressure is ______ L.
(Rounded off to the nearest integer)
[Given R = 0.0826 L atm K$$^{-1}$$ mol$$^{-1}$$]
Correct Answer: 5
We use the ideal gas equation $$PV = nRT$$ to find the volume of acetylene gas.
The molar mass of acetylene ($$C_2H_2$$) is $$2(12) + 2(1) = 26$$ g/mol.
Number of moles: $$n = \frac{4.75}{26} = 0.1827$$ mol.
Temperature: $$T = 50 + 273 = 323$$ K.
Pressure: $$P = \frac{740}{760}$$ atm $$= 0.9737$$ atm.
Applying the ideal gas law:
$$V = \frac{nRT}{P} = \frac{0.1827 \times 0.0826 \times 323}{0.9737}$$
$$V = \frac{0.1827 \times 26.68}{0.9737} = \frac{4.874}{0.9737} = 5.006 \text{ L}$$
Rounding off to the nearest integer, the volume is $$\textbf{5}$$ L.
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