Physics Grade 10 Gas laws Ideal gas law Worksheet markscheme

Worksheet markscheme

Cambridge 9702_s11_qp_42     Q2

1. (a) amount of substance                                                                               M1

containing same number of particles as in 0.012 kg of carbon-12                      A1                  [2]

(b) pV = nRT                                                                                                   C1

amount = (2.3 × 105 × 3.1 × 10–3) / (8.31 × 290)

+ (2.3 × 105 × 4.6 × 10–3) / (8.31 × 303)                                                           C1

= 0.296 + 0.420                                                                                                C1

= 0.716 mol                                                                                                      A1                  [4]

(give full credit for starting equation pV = NkT and N = nNA)

Cambridge 9702_s12_qp_41     Q2

2. (a) (i) either      random motion

               or            constant velocity until hits wall/other molecule                   B1                  [1]

(ii)   (total) volume of molecules is negligible                                                    M1

        compared to volume of containing vessel                                                A1

        or

        radius/diameter of a molecule is negligible                                                 (M1)

        compared to the average intermolecular distance                                    (A1)                   [2]

(b)   either      molecule has component of velocity in three directions

        or            c² = c_X² + c_Y² + c_Z²                                                                       M1

        random motion and averaging, so <c_X²> = <c_Y²> = <c_Z²>                              M1

        <c²> = 3<c_X²>                                                                                          A1

        so, pV = ⅓Nm<c²>                                                                                  A0                  [3]

(c)   <c²> ∝ T    or    c_rms ∝                                                                        C1

temperatures are 300 K and 373 K                                                                  C1

c_rms = 580 m s^–1                                                                                            A1                  [3]

(Do not allow any marks for use of temperature in units of ^oC instead of K)

Cambridge 9702_s04_qp_4              Q2

3. (a) mean (value of the) square                                                                     M1

of the speeds (velocities) of the atoms/particles/molecules                            A1               [2]

(b) (i) p = 1/3ρ<c²>                                                                                         C1

<c²> = 3 x 2 x 10⁵/2.4 = 2.5 x 10⁵                                                                       C1

r.m.s speed = 500 m s^-1                                                                                    A1              [3]

(ii) new <c²> = 1.0 x 10⁶ or <c²> increases by factor of 4                                      C1

<c²> ∝ T or 3/2 kT = 1/2 m<c²>                                                                     C1

T = {(1.0 x 10⁶) / (2.5 x 10⁵)} x 300

= 1200 K                                                                                                          A1              [3]