Find the number of moles in 2.00 L of gas at 35.0°C and under 7.41×107 N/m2 of pressure.
Select one:
a. 0.051 moles
b. 51 ×105 moles
c. 58 moles
d. 5.8 moles
58
58
To find the number of moles in a gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas in N/m2
V = volume of the gas in m3
n = number of moles
R = ideal gas constant (8.314 J/(mol·K))
T = temperature of the gas in Kelvin
First, let's convert the given temperature from degrees Celsius to Kelvin:
35.0°C + 273.15 = 308.15 K
Now we can plug in the values into the ideal gas law equation:
(7.41×107 N/m2) × (2.00 L) = n × (8.314 J/(mol·K)) × (308.15 K)
Simplifying:
7.41×107 N/m2 × 2.00 L = n × 8.314 J/(mol·K) × 308.15 K
148200000 N·L = n × 2554.057 J/K
To convert L to m3, we divide by 1000:
148200 m3 = n × 2554.057 J/K
Dividing both sides by 2554.057 J/K, we get:
n = 148200 m3 / 2554.057 J/K
Now we can calculate the value of n:
n = 57.990 moles
Therefore, the number of moles in 2.00 L of gas is approximately 58 moles.
The correct answer is option c. 58 moles.
To find the number of moles in a gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas (in Pascals)
V = volume of the gas (in cubic meters)
n = number of moles of the gas
R = ideal gas constant (8.314 J/(mol·K))
T = temperature of the gas (in Kelvin)
First, let's convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 35.0°C + 273.15 = 308.15 K
Next, let's convert the given pressure from N/m² to Pascals:
1 N/m² = 1 Pascal
So, the pressure is already in Pascals.
Now, we can rearrange the ideal gas law equation to solve for n (number of moles):
n = (PV) / (RT)
Plugging in the given values:
P = 7.41×10⁷ N/m²
V = 2.00 L = 0.002 m³
R = 8.314 J/(mol·K)
T = 308.15 K
n = (7.41×10⁷ N/m² * 0.002 m³) / (8.314 J/(mol·K) * 308.15 K)
Now, we can simplify the equation and calculate the value of n:
n = (1.482×10⁵ N * m) / (2561.1223 J)
n ≈ 0.0576 moles
Therefore, the number of moles in 2.00 L of gas at the given conditions is approximately 0.0576 moles.