Final answer:
To find the number of grams of Kr in a cylinder, the Ideal Gas Law is used. After converting the given temperature to Kelvin and using the Ideal Gas Law formula, the number of moles is calculated. These moles are then multiplied by krypton's molar mass to obtain the mass in grams.
Step-by-step explanation:
To calculate the number of grams of Kr (krypton) in a 4.80L cylinder at 78.0°C and 9.13 atm, we can use the Ideal Gas Law, which is PV = nRT. First, we need to convert the temperature to Kelvin by adding 273 to the Celsius temperature, and we need the value of R (the gas constant) to be in appropriate units that match the other given values. Here are the conversions:
- Temperature in Kelvin (T) = 78.0 + 273 = 351.0 K
- The gas constant (R) = 0.0821 L·atm/(K·mol)
Using the Ideal Gas Law and solving for n (the number of moles), we have:
n = (P * V) / (R * T) = (9.13 atm * 4.80 L) / (0.0821 L·atm/(K·mol) * 351.0 K)
After calculating the number of moles, we use the molar mass of krypton (approximately 83.798 g/mol) to find the mass in grams:
grams of Kr = number of moles * molar mass of krypton
Please note that you will need to use a calculator to find the numerical values for n and subsequently the mass in grams of krypton.