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Answer :
According to the ideal gas law, PV = nRT, pressure, volume, number of moles, and temperature are related to each other by the ideal gas constant (R). P = nRT/V, where n is the number of moles, R is the ideal gas constant, T is the temperature in Kelvin, and V is the volume. Let us first convert the volume of the canister from milliliters (mL) to liters (L):55.0 mL × (1 L/1000 mL) = 0.0550 L
Next, we need to calculate the number of moles of argon in the canister. We can use the molar mass of argon to convert from grams to moles:26.0 g Ar × (1 mol Ar/39.95 g Ar)
= 0.651 mol Ar Now we can use the ideal gas law to solve for pressure:P
= nRT/V
= (0.651 mol)(0.0821 L atm/mol K)(295 K)/(0.0550 L)
≈ 2.81 atm
Let's first convert the volume of a wine bottle from milliliters (mL) to liters (L):750.0 mL × (1 L/1000 mL) = 0.7500 LNext, let's convert the temperature to Kelvin:22.0°C + 273
= 295 KNow we can solve for the number of moles of argon required to fill a wine bottle at 1.20 atm and 295 K:P
= nRT/Vn
= PV/RT
= (1.20 atm)(0.7500 L)/(0.0821 L atm/mol K)(295 K)
≈ 0.0368 mol Ar Finally, we can use the number of moles in the canister to determine the maximum number of bottles that can be purged:n
= 0.651 mol Ar × (1 bottle/0.0368 mol Ar)
≈ 17.7 bottles (rounded down to the nearest whole number) Pressure of canister:
≈ 2.81 atm; Wine bottle count: 17
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