Final answer:
To find the volume of carbon dioxide at 10 °C and 120 atm, we can use the ideal gas law. Using the given density, we can find the molar mass of the gas, which allows us to find the number of moles. By using the ideal gas law equation PV = nRT, we can solve for the volume and find that it is 1317.68 L.
Step-by-step explanation:
We can use the ideal gas law to solve this problem. The ideal gas law equation is 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.
We are given the temperature of the carbon dioxide as 10 °C = 283 K, the pressure as 120 atm, and the density as 1.2 g/cm3. To find the volume, we need to find the number of moles of gas.
The density can be used to find the molar mass of the gas using the equation M = dRT/P, where M is the molar mass, d is the density, R is the ideal gas constant, and P is the pressure. Plugging in the given values, we get M = (1.2 g/cm3) * (0.0821 L*atm/mol*K) * (283 K) / (120 atm) = 2.82 g/mol.
Next, we can find the number of moles using the equation n = m/M, where m is the mass of the gas. Since we know the density and the volume, we can calculate the mass using the equation m = dV.
Plugging in the values, we get m = (1.2 g/cm3) * (V cm3), where V is the volume in cm3. The units will cancel out, and we get m = 1.2V g.
Finally, we can find the number of moles using the equation n = m/M. Plugging in the values, we get n = (1.2V g) / (2.82 g/mol) = 0.426V mol.
Now, we can use the ideal gas law equation PV = nRT to find the volume. Plugging in the values, we get (120 atm) * (V L) = (0.426V mol) * (0.0821 L*atm/mol*K) * (283 K).
Simplifying the equation, we have 120V = 0.0911V, which can be rearranged as 120V = 0.0911V * V, or 120 = 0.0911V. Solving for V, we find V = 1317.68 L.
Therefore, the volume of the carbon dioxide is 1317.68 L.