When 3.0g of carbon is burnt in 8.00g oxygen, 11.00g of carbon dioxide is produced. What mass of carbon dioxide will be formed when 3.00g of carbon is burnt in 50.0g of oxygen? Which law of chemical combination will govern your answer?
First we find the proportion of mass of carbon and oxygen in carbon dioxide.
In CO\(_2\) , C : O = 12 : 32 or 3 : 8
In other words,
we can say that
12.00 g carbon reacts with oxygen = 32.00 g
3.00 g carbon will react with oxygen = \(\frac{32}{12}\) x 3 = 8g
Therefore, 3.00 g of carbon will always react with 8.00 g of oxygen to form CO\(_2\) (11g), even if large amount (50.00 g) of oxygen is present.
This answer will be governed by ‘the law of constant proportions’.
Two circles intersect at two points B and C. Through B, two line segments ABD and PBQ are drawn to intersect the circles at A, D and P, Q respectively (see Fig. 9.27). Prove that ∠ACP = ∠ QCD

ABCD is a trapezium in which AB || CD and AD = BC (see Fig. 8.14). Show that
(i) ∠A = ∠B
(ii) ∠C = ∠D
(iii) ∆ABC ≅ ∠∆BAD
(iv) diagonal AC = diagonal BD [Hint : Extend AB and draw a line through C parallel to DA intersecting AB produced at E.]

(i) The kind of person the doctor is (money, possessions)
(ii) The kind of person he wants to be (appearance, ambition)