Any help would be great on the below problems. I am not sure where to begin. How do I solve these? Do I use a formula?

1. You are asked to make 500.0 mL of a 4.5M solution of HCl, but the only HCl you have available to dilute is 18.0M. Describe how you would make the desired solution. Show any math work and equations used.

2. A bag of potato chips contains 585 mL of air at 25°C and a pressure of 765 mmHg. Assuming the bag does not break, what will its volume be at the top of the mountain where the pressure is 442 mmHg and the temperature is 5.0°C? Show your work and equations used.

1. mL x M = mL x M

500 x 4.5 = mL x 18.0
Solve for mL of the 18.0. Remember volumes are not additive; therefore, you can't use 125 mL of the 18.0 M stuff and add 375 mL water. The way you do it is to place 125 mL of the 18.0 stuff in a 500 mL volumetric flask and add water to the mark.

2. (P1V1/T1) = (P2V2/T2)

P1V1/T1 = P2V2/T2

(765 mmHg)(585mL)/298K=(442mmHg) V2/278K
V2=944.55mL
so would that be right for #2??

Thank you so much for your help, I wasn't sure which law to use.

1. To make a 4.5M solution of HCl, you can use the dilution formula:

M1V1 = M2V2

Where:
M1 = initial concentration of the solution
V1 = initial volume of the solution
M2 = final concentration of the solution
V2 = final volume of the solution

Given:
M1 = 18.0M (initial concentration of the HCl)
V1 = ? (initial volume)
M2 = 4.5M (desired concentration of the solution)
V2 = 500.0 mL (desired final volume)

Using the dilution formula, we can solve for V1:

(18.0M)(V1) = (4.5M)(500.0 mL)

V1 = (4.5M)(500.0 mL) / (18.0M)

V1 = 125 mL

So, you need to take 125 mL of the 18.0M HCl and dilute it to a total volume of 500.0 mL by adding an appropriate amount of solvent (e.g., water).

2. To solve this problem, we can use the combined gas law:

P1V1 / T1 = P2V2 / T2

Where:
P1 = initial pressure of the gas
V1 = initial volume of the gas
T1 = initial temperature of the gas
P2 = final pressure of the gas
V2 = final volume of the gas
T2 = final temperature of the gas

Given:
P1 = 765 mmHg (initial pressure of the air in the bag)
V1 = 585 mL (initial volume of the air in the bag)
T1 = 25°C (initial temperature of the air in the bag)
P2 = 442 mmHg (final pressure at the top of the mountain)
V2 = ? (final volume at the top of the mountain)
T2 = 5.0°C (final temperature at the top of the mountain)

Rearranging the equation to solve for V2:

V2 = (P1 * V1 * T2) / (P2 * T1)

Plugging in the given values:

V2 = (765 mmHg * 585 mL * 5.0°C) / (442 mmHg * 25°C)

Remember to convert the temperatures to Kelvin (K) by adding 273:

V2 = (765 mmHg * 585 mL * 278 K) / (442 mmHg * 298 K)

Now, you can calculate the value of V2 by performing the necessary multiplication and division.

Sure, I'd be happy to help you solve these problems!

1. To make a 4.5M solution of HCl using the available 18.0M HCl, you will need to dilute the concentrated solution by adding an appropriate volume of solvent (usually water). The formula to calculate the volume of concentrated solution needed is:

C₁V₁ = C₂V₂

Where:
C₁ = Initial concentration of the concentrated HCl solution (18.0M)
V₁ = Volume of concentrated HCl solution needed
C₂ = Final concentration of the diluted HCl solution (4.5M)
V₂ = Final volume of the diluted HCl solution (500.0 mL)

Plugging in the values we have:
(18.0M)(V₁) = (4.5M)(500.0 mL)

Now solve for V₁:
V₁ = (4.5M)(500.0 mL) / (18.0M)

V₁ ≈ 125 mL

So you will need to take 125 mL of the 18.0M HCl solution and then dilute it with enough solvent (water) to make a total volume of 500.0 mL.

2. To solve this problem, you can use the ideal gas law, which states:

PV = nRT

Where:
P = Pressure
V = Volume
n = Number of moles of gas
R = Ideal gas constant
T = Temperature

Since the number of moles and the ideal gas constant remain constant, we can rearrange the equation as:

V₁ / T₁ = V₂ / T₂

Where:
V₁ = Initial volume of the air (585 mL)
T₁ = Initial temperature (25°C)
V₂ = Final volume of the air at the top of the mountain (unknown)
T₂ = Final temperature at the top of the mountain (5.0°C)

Now plug in the values we have:
(585 mL) / (25 + 273.15 K) = (V₂) / (5 + 273.15 K)

Solve for V₂:
V₂ = [(585 mL) / (25 + 273.15 K)] * (5 + 273.15 K)

V₂ ≈ 640.4 mL

So the volume of the bag of potato chips at the top of the mountain would be approximately 640.4 mL.