what is the volume at STP of a sample of CO2 that has a volume of 75.0 ML at 30c and 680 mm Hg
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To find the volume of a sample of CO2 at Standard Temperature and Pressure (STP), we need to use the Ideal Gas Law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature
First, we need to convert the given values to the appropriate units:
- Volume: 75.0 mL (milliliters) needs to be converted to liters. There are 1000 mL in 1 L, therefore:
Volume = 75.0 mL ÷ 1000 = 0.075 L
- Temperature: 30°C needs to be converted to Kelvin (K). To convert Celsius to Kelvin:
Temperature in Kelvin = Temperature in °C + 273.15
Temperature in Kelvin = 30 + 273.15 = 303.15 K
- Pressure: 680 mm Hg needs to be converted to atmospheres (atm). There are 760 mm Hg in 1 atm, therefore:
Pressure = 680 mm Hg ÷ 760 = 0.895 atm
Now we can plug these values into the Ideal Gas Law equation and solve for the moles of CO2:
PV = nRT
(0.895 atm) * (0.075 L) = n * (0.0821 L·atm/(mol·K)) * (303.15 K)
0.067125 = n * 24.901215
n = 0.067125 / 24.901215
n ≈ 0.002699 mol
Finally, since we are looking for the volume at STP (Standard Temperature and Pressure), STP is defined as a temperature of 0°C (273.15 K) and a pressure of 1 atm. We can use the obtained number of moles to find the volume at STP using the Ideal Gas Law:
PV = nRT
(1 atm) * V = (0.002699 mol) * (0.0821 L·atm/(mol·K)) * (273.15 K)
V = (0.002699 mol) * (0.0821 L·atm/(mol·K)) * (273.15 K) / (1 atm)
V ≈ 0.0562 L
Therefore, the volume of the sample of CO2 at STP is approximately 0.0562 liters.
To find the volume of the sample of CO2 at STP (Standard Temperature and Pressure), we need to use the ideal gas law equation:
PV = nRT
where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature in Kelvin
To solve the problem, we need to manipulate the given information and use various gas laws to convert the values to the correct units. Here's a step-by-step process to find the volume at STP:
Step 1: Convert temperature from Celsius to Kelvin.
To convert Celsius to Kelvin, we use the formula:
T(K) = T(°C) + 273.15
So, T(K) = 30°C + 273.15 = 303.15 K
Step 2: Convert pressure from mm Hg to atm.
Since we are using the ideal gas constant R, we need to express the pressure in atmospheres (atm). To convert mm Hg to atm, we use the conversion factor:
1 atm = 760 mm Hg
So, pressure in atm = 680 mm Hg / 760 mm Hg/atm = 0.8947 atm (rounded to 4 decimal places).
Step 3: Convert volume from mL to liters.
Since the ideal gas law equation requires volume in liters, we need to convert milliliters (mL) to liters (L). To do this, we use the conversion factor:
1 L = 1000 mL
So, volume in liters = 75.0 mL / 1000 mL/L = 0.075 L
Now, we have the following values:
P = 0.8947 atm
V = 0.075 L
T = 303.15 K
Step 4: Calculate the number of moles.
Using the ideal gas law equation, we can rearrange it to solve for the number of moles (n):
n = PV / RT
Substituting the values:
n = (0.8947 atm) * (0.075 L) / [(0.0821 L*atm/(mol*K) * 303.15 K]
We can simplify this calculation to find the number of moles of CO2.
Step 5: Calculate the volume at STP.
At STP, the temperature is 273.15 K, and the pressure is 1 atm. To find the volume at STP, we can use the relationship between the initial and final conditions of n, T, and P:
V1 / n1 = V2 / n2
Substituting the given and calculated values:
V1 = 0.075 L
n1 = number of moles calculated in Step 4
T1 = 303.15 K
P1 = 0.8947 atm
T2 = 273.15 K
P2 = 1 atm
Solving for V2 (volume at STP):
V2 = (V1 / n1) * (n2 * P2 * T1) / (n1 * P1 * T2)
Substitute the values calculated in Step 4 and the STP conditions into this equation and evaluate to find the volume at STP.