Dry ice is frozen carbon dioxide. If you have 1.4kg of dry ice, what volume will it occupy if you heat it enough to turn it into a gas at a temperature of 20 degrees Celsius? (answer is in m^3)
PV=nRT
n=number of moles=1400/44
R is universal gas constant
T=20+273
P=101.3kpa
solve for V
0.55 cubic meters
A child applies a force F? parallel to the x -axis to a 10.0-kg sled moving on the frozen surface of a small pond. As the child controls the speed of the sled, the x -component of the force she applies varies with the x -coordinate of the sled as shown in the figure (Figure 1) Part A Calculate the work done by the force F? when the sled moves from x=0 to x=8.0m. Express your answer using two significant figures. Part B Calculate the work done by the force F? when the sled moves from x=8.0m to x =12.0m. Express your answer using two significant figures. Part C Calculate the work done by the force F? when the sled moves from x=0 to x =12.0m. . Express your answer using two significant figures.
To find the volume of 1.4 kg of dry ice when it turns into a gas at 20 degrees Celsius, we need to know the density of carbon dioxide gas at that temperature and pressure.
Step 1: Determine the molar mass of carbon dioxide (CO2).
Carbon has an atomic mass of approximately 12 g/mol, and oxygen has an atomic mass of approximately 16 g/mol. Since carbon dioxide (CO2) consists of one carbon atom and two oxygen atoms, the molar mass of CO2 is calculated as:
CO2 = (1 * 12 g/mol) + (2 * 16 g/mol) = 44 g/mol
Step 2: Calculate the number of moles in 1.4 kg of dry ice.
The number of moles (n) is calculated using the relationship between mass (m) and molar mass (M) of a substance:
n = m / M
Converting the mass of dry ice from kilograms to grams:
1.4 kg = 1,400 g
Substituting the values into the formula:
n = 1,400 g / 44 g/mol ≈ 31.81 mol
Step 3: Convert moles to volume using the ideal gas law.
The ideal gas law equation is:
PV = nRT
Where:
P is the pressure (in Pascals),
V is the volume (in m^3),
n is the number of moles,
R is the gas constant (8.314 J/(mol·K)),
T is the temperature (in Kelvin).
We need to convert the given temperature from Celsius to Kelvin:
T (Kelvin) = 20 + 273.15 ≈ 293.15 K
Assuming the pressure remains constant, we can rearrange the ideal gas law equation to solve for V:
V = nRT / P
Step 4: Substitute the values into the ideal gas law equation.
P (pressure) is not given, but assuming standard atmospheric pressure at sea level (1 atmosphere or 101,325 Pascals) will suffice for this calculation:
V = (31.81 mol) * (8.314 J/(mol·K)) * (293.15 K) / (101,325 Pa) ≈ 0.716 m^3
Therefore, when 1.4 kg of dry ice turns into a gas at 20 degrees Celsius, it will occupy approximately 0.716 cubic meters (m^3).