1500 cm3 of ideal gas at STP is cooled to -20°C and put into a 1000 cm3 container. What is the final gauge pressure?
11 kPa
40 kPa
113 kPa
141 kPa
240 kPa
absolute pressure=101.3kpa(273-20)/273*1500/1000
Gauge pressure=absolute-atmospheric.
determine
So just estiamting, answer b is in the ballpark.
a liter is 10^3 = 1000 cm^3
so we have 22.4 * 1.5 = 33.6 moles of gas at 273 deg K and 100 kPa
P V = n R T
n and r remain the same
so
P1V1/T1 = P2V2/T2
100 (1500)/273 = P2 (1000)/253
P2 = 139 kPa ABSOLUTE pressure
- 100 KPa for gage
= 39 k Pa gage
To solve this problem, we can use the ideal gas law:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature
At STP (Standard Temperature and Pressure), the temperature is 0°C (or 273 K) and the pressure is 1 atm.
Since both the initial and final temperatures are given in Celsius, we need to convert them to Kelvin by adding 273.
Initial conditions:
V1 = 1500 cm^3
T1 = 0°C + 273 = 273 K
P1 = 1 atm
Final conditions:
V2 = 1000 cm^3
T2 = -20°C + 273 = 253 K
P2 = ?
First, we can calculate the number of moles using the ideal gas law:
n1 = (P1 * V1) / (R * T1)
n2 = (P2 * V2) / (R * T2)
Since the amount of gas does not change, n1 = n2. Therefore:
(P1 * V1) / (R * T1) = (P2 * V2) / (R * T2)
We can isolate P2:
P2 = (P1 * V1 * T2) / (V2 * T1)
Substituting the values:
P2 = (1 atm * 1500 cm^3 * 253 K) / (1000 cm^3 * 273 K)
P2 = 113 kPa
Therefore, the final gauge pressure is 113 kPa.
To find the final gauge pressure, we need to use the ideal gas law. The ideal gas law states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
First, we need to convert the initial volume of the gas to liters:
1500 cm^3 = 1500/1000 = 1.5 L
Next, we need to convert the temperature from Celsius to Kelvin:
T = -20 + 273 = 253 K
Since the gas is an ideal gas, we can assume that the number of moles (n) and the gas constant (R) are constant.
Now, let's set up the equation to find the final pressure:
(P_1 * V_1) / T_1 = (P_2 * V_2) / T_2
Where:
P_1 = initial pressure in atmospheric pressure (STP is 1 atm)
V_1 = initial volume in liters (1.5 L)
T_1 = initial temperature in Kelvin (273 K)
P_2 = final pressure in atmospheric pressure (what we want to find)
V_2 = final volume in liters (1000 cm^3 = 1 L)
T_2 = final temperature in Kelvin (253 K)
Now, let's substitute the values into the equation:
(1 * 1.5) / 273 = (P_2 * 1) / 253
Simplifying the equation:
1.5 / 273 = P_2 / 253
Cross-multiplying:
1.5 * 253 = 273 * P_2
P_2 = (1.5 * 253) / 273
P_2 ≈ 1.392 atm
To convert from atm to kilopascals (kPa), we multiply by 101.325:
P_2 ≈ 1.392 * 101.325 ≈ 141 kPa
Therefore, the final gauge pressure is approximately 141 kPa.