To answer this question, we'll use the Ideal Gas Law, which can be expressed as:
PV = nRT
Where:
P = pressure (in atmospheres, atm)
V = volume (in liters, L)
n = number of moles of gas
R = universal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin, K)
First, we need to convert the given temperature from Celsius to Kelvin because the Ideal Gas Law requires temperature to be in Kelvin:
T(K) = T(°C) + 273.15
T(K) = 17.0°C + 273.15 = 290.15 K
Now, we have:
P = 0.764 atm
n = 0.00911 mol
R = 0.0821 L·atm/mol·K
T = 290.15 K
Plug these values into the Ideal Gas Law equation to solve for V:
0.764 atm V = 0.00911 mol 0.0821 L·atm/mol·K 290.15 K
Now, calculate the volume (V):
V = (0.00911 mol 0.0821 L·atm/mol·K 290.15 K) / 0.764 atm
V ≈ (0.00911 mol 0.0821 L·atm/mol·K 290.15 K) / 0.764 atm
V ≈ (0.00911 0.0821 290.15) / 0.764
V ≈ 0.218406175 L
Since the question asks for the volume in milliliters, we'll convert liters to milliliters (1 L = 1000 mL):
V = 0.218406175 L 1000 mL/L ≈ 218.41 mL
Therefore, the volume the gas will occupy if it is collected at 17.0°C and 0.764 atm pressure is approximately 218.41 mL.
