5. Ammonium carbonate decomposes upon heating according to the following equatio

Question

5. Ammonium carbonate decomposes upon heating according to the following equation: (NH4)2CO3 (s) 2NH3 (g) + CO2 (g) + H2O (g). Calculate the total volume of gas produced at 22 °Cand 1.02 atm by complete decomposition of 11.83 g of ammonium carbonate.

6. A scuba diver creates a spherical bubble with r = 2.5 cm at a depth of 30.0 m where the totalpressure (including atmospheric pressure) is 4.00 atm. What is the radius of the bubble when itreaches the surface of the water? Assume atmospheric pressure to be 1.00 atm, and the temperature is 298 K.

Explanation / Answer

Answer – 5) We are given , mass of (NH4)2CO3 = 11.83 g

Reaction - (NH4)2CO3 (s) -------> 2NH3 (g) + CO2 (g) + H2O (g)

We need to calculate moles of ammonium carbonate first

Moles of ammonium carbonate = 11.83 g / 96.09 g

                                                   = 0.123 moles

Now we need to calculate the moles of each gas product from this moles

From the above balanced equation

1 moles of (NH4)2CO3 (s) = 2 NH3 (g)

So, 0.123 moles of (NH4)2CO3 (s) = ?

= 0.246 molesof NH3

The mole of CO2 (g) = moles of H2O (g) = moles of (NH4)2CO3 (s) = 0.123 moles

So, total moles of gases = 0.246 + 0.123 + 0.123

                                     = 0.492 moles

T = 22+273 = 295 K, P = 1.02 atm

So using the Ideal gas law

PV = nRT

V = nRT / P

   = 0.492 moles * 0.0821 L.atm.mol.K-1 * 295 K / 1.02atm

= 11.69 L

So total volume of gases is 11.69 L

6) We are given, spherical bubble with r = 2.5 cm at a depth of 30.0 m , total pressure = 4.00 atm

, at the surface pressure = 1.00 atm

First we need to calculate the volume of the spherical bubble

We know formula

V = 4/3**r3

    = 4/3*3.14* (2.5 cm)3

    = 65.42 cm3

1 cm3 = 1 mL

So, 65.42 cm3 = 65.42 mL

Now we need to calculate volume of the spherical bubble at surface

P1 = 4.00 atm, V1 = 65.42 mL , P2 = 1.00 atm , V2 = ?

So using the Boyles law

P1V1 = P2V2

So, V2 = P1V1/P2

            = 4.00 atm * 65.42 mL / 1.00 mL

            = 261.66 mL or cm3

Now we need to calculate eh radius form this volume

V = 4/3**r3

r3 = 3V/4

   = 3* 261.66 cm3 / 4*3.14

= 62.5 cm3

By taking the cube root from both side

r = 3.97 cm

so, the radius of the bubble when it reaches the surface of the water is 3.97 cm

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