Final answer:
To determine the amount of helium, we converted the given values to appropriate units, applied the ideal gas law to find the number of moles, and then multiplied by the molar mass of helium to find the mass in grams, which is approximately 0.012232 g of He.
Step-by-step explanation:
To find out how many grams of helium (He) were used, given that the helium in the abdomen produces a pressure of 18 mmHg and a volume of 3.4 L at 26 °C, we can use the ideal gas law equation PV = nRT. Here, P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
First, convert the given temperature to Kelvin:
Temperature in Kelvin (K) = 26 °C + 273.15
= 299.15 K.
Next, convert the pressure from mmHg to atm, as the gas constant R value used here is in atm:
Pressure in atm = 18 mmHg × (1 atm / 760 mmHg)
= 0.02368 atm.
Now we can calculate the number of moles (n):
P×V = n×R×T
0.02368 atm × 3.4 L = n × 0.0821 L·atm/(mol·K) × 299.15 K
n = (0.02368 atm × 3.4 L) / (0.0821 L·atm/(mol·K) × 299.15 K)
n ≈ 0.003058 mol of He
Finally, to get the mass in grams, multiply the moles by the molar mass of helium (4.00 g/mol):
Mass of He = 0.003058 mol × 4.00 g/mol
= 0.012232 g of He.