The molar mass of Neon is 20.18 g/mole. If 100.0 g of Ne is compressed into a glass tube at a pressure of 1480 mmHg and a temperature of 30°C, what will be the final volume of the gas?
The correct answer and explanation is :
To calculate the final volume of the Neon (Ne) gas under the given conditions, we will use the Ideal Gas Law equation, which is:
$$
PV = nRT
$$
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 gas,
- $R$ is the ideal gas constant (0.0821 L·atm/(mol·K)),
- $T$ is the temperature of the gas in Kelvin (K).
Step 1: Convert all units to appropriate SI units
- Pressure (P): 1480 mmHg must be converted to atmospheres (atm). The conversion factor is:
$$
1 \text{ atm} = 760 \text{ mmHg}
$$
Thus:
$$
P = \frac{1480 \text{ mmHg}}{760 \text{ mmHg/atm}} = 1.947 \text{ atm}
$$
- Temperature (T): The temperature is given as 30°C. To convert to Kelvin, we use:
$$
T(K) = T(°C) + 273.15 = 30 + 273.15 = 303.15 \text{ K}
$$
- Mass of Neon (Ne): The mass of Neon is 100.0 g. The molar mass of Neon is 20.18 g/mol, so the number of moles ($n$) is:
$$
n = \frac{100.0 \text{ g}}{20.18 \text{ g/mol}} = 4.96 \text{ mol}
$$
Step 2: Use the Ideal Gas Law to solve for volume (V)
Rearrange the Ideal Gas Law equation to solve for $V$:
$$
V = \frac{nRT}{P}
$$
Substitute the known values:
$$
V = \frac{(4.96 \text{ mol})(0.0821 \text{ L·atm/mol·K})(303.15 \text{ K})}{1.947 \text{ atm}}
$$
Step 3: Calculate the volume
Now, calculate the volume:
$$
V = \frac{(4.96)(0.0821)(303.15)}{1.947} = \frac{123.55}{1.947} = 63.5 \text{ L}
$$
Final Answer:
The final volume of Neon gas under the given conditions is approximately 63.5 L.
Explanation:
This calculation utilizes the Ideal Gas Law, which relates the pressure, volume, number of moles, and temperature of a gas. In this scenario, we were provided with the mass of Neon, from which we calculated the number of moles. By converting the pressure to atmospheres and the temperature to Kelvin, we could substitute these values into the Ideal Gas Law equation to solve for the volume. The volume represents the space that 100.0 grams of Neon would occupy when compressed to the specified pressure and temperature.