If the condition on 166cm^3 gas at 93000kpa and 15° are increased by 7kp and 5°c, what will be the new volume of the gas in liter?
We can use the combined gas law formula to solve this problem:
(P1V1/T1) = (P2V2/T2)
Where:
P1 = 93000 kPa (initial pressure)
V1 = 166 cm^3 (initial volume)
T1 = 15°C + 273.15 = 288.15 K (initial temperature in Kelvin)
P2 = 93000 kPa + 7 kPa = 93007 kPa (final pressure)
T2 = 15°C + 5°C + 273.15 = 293.15 K (final temperature in Kelvin)
V2 = ? (final volume)
Substituting the values:
(93000 x 166/288.15) = (93007 x V2/293.15)
Simplifying:
V2 = (93000 x 166 x 293.15) / (288.15 x 93007)
V2 = 169.31 cm^3
Converting to liters:
V2 = 0.16931 L
Therefore, the new volume of the gas at 93007 kPa and 20°C is 0.16931 L.
To find the new volume of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas in pascals (Pa)
V is the volume of the gas in cubic meters (m^3)
n is the number of moles of gas
R is the ideal gas constant (8.314 J/(mol·K))
T is the temperature of the gas in Kelvin (K)
First, we need to convert the initial volume from cubic centimeters (cm^3) to liters (L):
166 cm^3 = 0.166 L
Next, we need to convert the pressure from kilopascals (kPa) to pascals (Pa):
93000 kPa = 93000 * 1000 Pa = 93000000 Pa
Now, let's calculate the initial number of moles of gas. Since we don't have the molar mass or mass of the gas, we cannot find the exact number of moles. However, we can assume the gas behaves ideally and use the ideal gas law to find the number of moles:
PV = nRT
n = PV / RT
Assuming the gas is at standard temperature and pressure (STP) conditions (0°C or 273.15 K and 1 atm or 101325 Pa), we can calculate the number of moles at STP:
n = (93000000 Pa * 0.166 L) / (8.314 J/(mol·K) * 273.15 K) = 215.5 mol
Next, we need to convert the change in pressure and temperature to pascals (Pa) and Kelvin (K), respectively:
Increase in pressure: 7 kPa = 7 * 1000 Pa = 7000 Pa
Increase in temperature: 5 °C = 5 K
Now, let's calculate the new pressure and temperature using the increased values:
New Pressure = 93000000 Pa + 7000 Pa = 93007000 Pa
New Temperature = 15 °C + 5 K = 20 °C = 20 + 273.15 K = 293.15 K
Finally, we can use the ideal gas law to find the new volume:
New Volume = (n * R * New Temperature) / New Pressure
V = (215.5 mol * 8.314 J/(mol·K) * 293.15 K) / 93007000 Pa
Calculating this expression gives:
New Volume ≈ 11.22 L
Therefore, the new volume of the gas, when the condition is increased by 7 kPa and 5 °C, is approximately 11.22 liters.