Answer :
According to the given statement 16.2 L is the balloon’s volume at 22°C and a pressure of 742 mmHg.
The correct option is C.
What is the volume?
Volume is a unit used to describe how much space a substance takes up. A physical material with mass and space-occupying properties is referred to as matter. The common unit of volume in physical sciences like chemistry is the cubic metre.
Briefing:
PV=nRT
P is the pressure
V is the volume
n is the number of moles
R is the gas constant
T is the temperature
Calculating n:
n= mass/molar mass of carbon dioxide
n = 28.8/44
n = 0.6545 mol
T = 22C⁰ + 273
T = 295 K
P = 742mmHg * 1atm/760mmHg
P = 0.976315 mmHg
R=0.0821 L atm/mol.K
V = nRT/P
V = 0.6545 * 0.0821 * 295/0.976315
V = 16.2 L
Volume of the balloon at a temperature of 22⁰ C is 16.2 L.
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To find the volume of the balloon after sublimation of dry ice, we use the Ideal Gas Law. For 28.8 g of dry ice, we have 0.654 mol CO₂, which gives us a volume of approximately C. 16.2 L at 22°C and 742 mmHg.
To calculate the volume of the balloon after the sublimation of dry ice (solid CO₂), we should use the Ideal Gas Law, which is expressed as PV = nRT. First, we need to find the number of moles of CO₂ which is done by dividing the mass of the dry ice by its molar mass. The molar mass of CO₂ is 44.01 g/mol. So, for 28.8 g of CO₂, we have:
n = mass / molar mass = 28.8 g / 44.01 g/mol = 0.654 mol of CO₂
Next, we convert the given temperature to Kelvin by adding 273.15 to the Celsius temperature (T = 22 "+" 273.15 = 295.15 K) and the pressure from mmHg to atmospheres (1 atm = 760 mmHg, so P = 742 mmHg / 760 mmHg/atm ≈ 0.976 atm).
Now we apply the Ideal Gas Law:
PV = nRT
Rearranging for V, we get:
V = (nRT) / P
V = (0.654 mol × 0.0821 L×atm/mol×K × 295.15 K) / 0.976 atm V ≈ 16.5 L
Therefore, the volume of the balloon is closest to 16.2 L, which is option C.
