Question

1. which of the following factors affects the rate of diffusion of a gas?

a. number of atoms
b. number of molecules
c. viscosity
d. surface tension

1. two points q and r in a room are specified by the coordinates (0, 0, 0) and (1, 1, 1) respectively. determine the distance qr in metres.

a. 1
b. √2
c. √3
d. 3

1. the relative density of ice is 0.9. this statement implies that when a given mass of ice melts the

a. volume of water formed would be 0.9 times that of the ice.
b. volume of water formed would be 0.9 more than that of the ice.
c. mass of water formed would be 0.9 times that of the ice.
d. mass of water formed would be 0.9 less than that of the ice.

1. the pressure at a point in a liquid depends on the

i. cross-sectional area of the vessel containing the liquid.
ii. depth below the surface of the liquid.
iii. density of the liquid.
which of the statements above are correct?
a. i and ii only
b. i and iii only
c. ii and iii only
d. i, ii and iii

Explanation:

Question 1

To determine the factor affecting gas diffusion rate, recall Graham's law and gas properties. Viscosity (B) relates to fluid flow resistance, not gas diffusion. Surface tension (C) is a liquid property. Number of atoms (A) isn't a direct factor. Wait, correction: Gas diffusion rate depends on molar mass (related to number of molecules? No, molar mass. But among options, viscosity is for fluids, surface tension for liquids. Wait, maybe I made a mistake. Wait, the options: A: Number of atoms – no. B: Viscosity – viscosity of gas? Wait, maybe the question has a typo, but among options, the correct factor for gas diffusion (from Graham's law: molar mass, which relates to number of molecules? Wait, no. Wait, maybe the intended answer is related to molecular properties. But among the options, the correct one: Wait, maybe the options are miswritten, but typically, factors affecting gas diffusion are molar mass, temperature, pressure. But among the given options, the best is none? No, maybe the question is about liquid? No, it's gas. Wait, maybe the answer is B? No, viscosity is for fluids. Wait, maybe the question is incorrect, but following the options, the intended answer is likely B? No, I think I messed up. Wait, let's re-express: Gas diffusion rate (Graham's law: rate ∝ 1/√molar mass). Molar mass is related to number of molecules (molar mass = mass/moles, moles = number of molecules/NA). So number of molecules (A) – no, molar mass. But among options, the only one related to gas properties? Wait, viscosity of gas is a property, but does it affect diffusion? Diffusion in gas: the rate is affected by molar mass, temperature, pressure. Viscosity is internal friction, but maybe the question considers viscosity as a factor? No, I think the correct answer is A? No, number of atoms. Wait, maybe the question is wrong, but let's check standard questions. Typically, factors affecting gas diffusion: molar mass (related to molecular weight), temperature, pressure. Among the options, the closest is A (number of molecules, since molar mass depends on molecular weight, which is related to number of atoms/molecules). But I'm confused. Wait, maybe the answer is B? No, viscosity is for liquids. Wait, maybe the question is about liquid diffusion? No, it's gas. Hmm.

Step1: Recall distance formula in 3D

The distance between two points \((x_1,y_1,z_1)\) and \((x_2,y_2,z_2)\) is \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}\).

Step2: Substitute coordinates

For \(Q(0,0,0)\) and \(R(1,1,1)\), \(x_2 - x_1 = 1 - 0 = 1\), \(y_2 - y_1 = 1 - 0 = 1\), \(z_2 - z_1 = 1 - 0 = 1\).
So \(d = \sqrt{(1)^2 + (1)^2 + (1)^2} = \sqrt{1 + 1 + 1} = \sqrt{3}\). Wait, no: wait, \((1)^2 + (1)^2 + (1)^2 = 3\), so \(\sqrt{3}\)? But wait, no: wait, the options have \(\sqrt{3}\) as option C? Wait, the options are A:1, B:\(\sqrt{2}\), C:\(\sqrt{3}\), D:3. Wait, my calculation: \(\sqrt{(1-0)^2 + (1-0)^2 + (1-0)^2} = \sqrt{1 + 1 + 1} = \sqrt{3}\), so option C.

Relative density (RD) of ice = 0.9 means \(\text{RD} = \frac{\text{density of ice}}{\text{density of water}} = 0.9\), so \(
ho_{\text{ice}} = 0.9
ho_{\text{water}}\). Mass is conserved: \(m_{\text{ice}} = m_{\text{water}}\). Using \(m =
ho V\), \(
ho_{\text{ice}} V_{\text{ice}} =
ho_{\text{water}} V_{\text{water}} \). Substituting \(
ho_{\text{ice}} = 0.9
ho_{\text{water}}\), we get \(0.9
ho_{\text{water}} V_{\text{ice}} =
ho_{\text{water}} V_{\text{water}}\), so \(V_{\text{water}} = 0.9 V_{\text{ice}}\)? No, wait: \(V_{\text{water}} = \frac{
ho_{\text{ice}}}{
ho_{\text{water}}} V_{\text{ice}} = 0.9 V_{\text{ice}}\)? Wait, no: \(
ho_{\text{ice}} = 0.9
ho_{\text{water}}\), so \(V_{\text{water}} = \frac{m}{
ho_{\text{water}}}\), \(V_{\text{ice}} = \frac{m}{
ho_{\text{ice}}} = \frac{m}{0.9
ho_{\text{water}}}\). So \(V_{\text{water}} = 0.9 V_{\text{ice}}\)? Wait, no: \(V_{\text{water}} = \frac{m}{
ho_{\text{water}}}\), \(V_{\text{ice}} = \frac{m}{0.9
ho_{\text{water}}}\), so \(V_{\text{water}} = 0.9 V_{\text{ice}}\) (since \(V_{\text{ice}} = \frac{m}{0.9
ho_{\text{water}}} = \frac{10}{9} \frac{m}{
ho_{\text{water}}} = \frac{10}{9} V_{\text{water}}\), so \(V_{\text{water}} = 0.9 V_{\text{ice}}\)). Wait, but the options: A: volume of water is 0.9 times ice? No, wait, no: if ice is less dense than water, when it melts, volume decreases. Wait, ice density is 0.9 g/cm³, water is 1 g/cm³. So mass of ice = mass of water. Let mass be m. Volume of ice: \(V_{\text{ice}} = \frac{m}{0.9}\), volume of water: \(V_{\text{water}} = \frac{m}{1}\). So \(V_{\text{water}} = 0.9 V_{\text{ice}}\) (since \(V_{\text{ice}} = \frac{m}{0.9}\), so \(0.9 V_{\text{ice}} = m = V_{\text{water}}\)). So the volume of water is 0.9 times that of ice? Wait, no: \(V_{\text{water}} = 0.9 V_{\text{ice}}\) means water volume is less than ice? But ice melts to water, volume decreases. Wait, yes: ice has larger volume than water of same mass. So if \(V_{\text{ice}} = \frac{m}{0.9}\), \(V_{\text{water}} = \frac{m}{1}\), so \(V_{\text{water}} = 0.9 V_{\text{ice}}\) (because \(V_{\text{ice}} = \frac{10}{9} V_{\text{water}}\), so \(V_{\text{water}} = \frac{9}{10} V_{\text{ice}} = 0.9 V_{\text{ice}}\)). So option B: "volume of water formed would be 0.9 times that of the ice" – no, wait, no: \(V_{\text{water}} = 0.9 V_{\text{ice}}\) means water volume is 0.9 times ice volume, which is correct (since ice volume is larger). Wait, but the options: A: "volume of water formed would be 0.9 times more than that of the ice" – no, more would be 1.9 times. B: "volume of water formed would be 0.9 times that of the ice" – yes, that's correct. Wait, but let's check the options again:

A. volume of water formed would be 0.9 times more than that of the ice. (0.9 more means 1.9 times, wrong)

B. volume of water formed would be 0.9 times that of the ice. (correct, as \(V_{\text{water}} = 0.9 V_{\text{ice}}\))

C. mass of water formed would be 0.9 times that of the ice. (mass is conserved, so equal, wrong)

D. mass of water formed would be 0.9 less than that of the ice. (mass is conserved, wrong)

So correct answer is B.

Answer:

A. Number of atoms (Note: This might be a flawed question, but based on options, this is a possible intended answer. Alternatively, if considering molecular properties, number of molecules relates to molar mass, which affects diffusion rate via Graham's law.)

Question 2