3. At 34.0°C, the pressure inside a nitrogen-filled tennis ball with a volume of 148 cm3 is 212 kPa. How many moles of N2 are in the tennis ball?

0.0123 mol

Explanation:

Step 1: Convert 34.0 °C to Kelvin

We will use the following expression.

K = °C + 273.15 = 34.0 + 273.15 = 307.2 K

Step 2: Convert 148 cm³ to L

We will use the conversion factors:

Step 3: Convert 212 kPa to atm

We will use the conversion factor 1 atm = 101.325 kPa.

212 kPa × 1 atm / 101.325 kPa = 2.09 atm

Step 4: Calculate the moles of nitrogen gas

We will use the ideal gas equation.

P × V = n × R × T

n = P × V / R × T

n = 2.09 atm × 0.148 L / (0.0821 atm.L/mol.K) × 307.2 K = 0.0123 mol

the density of gold = 19.3 g/cm3

the relation between density and mass and volume is

density = mass / volume

given :

mass of gold = 13 g

density = 13g / volume = 19.3

volume = 13 /19.3 = 0.67 cm^3

thus volume of gold nugget = 0.67 cm^3

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