Answer :
The number of moles of N₂ in the 2.82 L cylinder at 66.9 °C and 7.33 atm is approximately 0.754 moles.
To calculate the number of moles of N₂ in a cylinder, we can use the ideal gas law equation, which relates the pressure, volume, number of moles, and temperature of a gas. The equation is given as follows:
PV = nRT
where:
- P is the pressure of the gas in atmospheres (atm),
- V is the volume of the gas in liters (L),
- n is the number of moles of the gas,
- R is the ideal gas constant (0.0821 L·atm/(mol·K)), and
- T is the temperature of the gas in Kelvin (K).
To begin, we need to convert the temperature from Celsius to Kelvin. The Kelvin temperature scale is an absolute temperature scale that starts at 0 K, which is equivalent to -273.15 °C. To convert Celsius to Kelvin, we add 273.15 to the Celsius temperature. In this case, the Celsius temperature is given as 66.9 °C, so the temperature in Kelvin is:
T(K) = T(°C) + 273.15
T(K) = 66.9 °C + 273.15 = 340.05 K
Now that we have the temperature in Kelvin, we can proceed with the ideal gas law equation and solve for the number of moles (n):
n = PV / RT
Substituting the given values:
P = 7.33 atm (given pressure)
V = 2.82 L (given volume)
R = 0.0821 L·atm/(mol·K) (ideal gas constant)
T = 340.05 K (temperature in Kelvin)
Plugging these values into the equation, we get:
n = (7.33 atm × 2.82 L) / (0.0821 L·atm/(mol·K) × 340.05 K)
Simplifying the equation, we find:
n ≈ 0.754 moles
Therefore, there are approximately 0.754 moles of N₂ in the 2.82 L cylinder at a temperature of 66.9 °C and a pressure of 7.33 atm.
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