A Gas Volume Calculation Dilemma

How can we calculate the volume of a gas at STP based on given pressure, temperature, and initial volume values?

Calculating Gas Volume at STP

To calculate the volume of a gas at standard temperature and pressure (STP), we can use the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. In this case, we are given:

Pressure (P) = 576 mmHg
Temperature (T) = 44.0°C = 317.15 K
Volume (V) = 6.17 L

To find the volume at STP, we first need to determine the number of moles of the gas. Using the ideal gas law equation:
n = PV / RT

Substitute the given values into the equation:
n = (576 mmHg * 6.17 L) / (0.0821 L·atm/mol·K * 317.15 K)

Calculating the number of moles:
n ≈ 1.53 mol

Since the number of moles remains constant at STP, we can use it to calculate the volume at STP. The temperature at STP is 273.15 K and the pressure is 1 atm. Applying the ideal gas law equation:
V(STP) = nRT / P(STP)

Substitute the values:
V(STP) = (1.53 mol * 0.0821 L·atm/mol·K * 273.15 K) / 1 atm

After simplifying the equation:
V(STP) ≈ 34.13 L

Therefore, the approximate volume of the gas at STP is 34.13 L.

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