How many moles of chlorine gas are present under ideal conditions at 25 degrees C, 762 torr, with a volume of 14.2 L?
Here we have an ideal gas, which means that we can use the ideal gas law: PV=nRT Where P is the pressure, V is volume, n is number of moles, R is the ideal gas constant, and T is the temperature. In problems like these the main focus is to make sure your units line up. We will use the ideal gas constant R=0.08206 L atm/mol K, which can be found in any chemistry text. This means we will have to convert our pressure to atmosphere and temperature to Kelvin. Temperature conversions are simple so we will start with that. Celsius to Kelvin is T(deg C) + 273 = K. Our temperature of 25 deg C + 273 = 298 K. Find your conversion for torr to atmosphere. It should read 760 torr = 1 atm. 762 torr x 1 atm/760 torr = 1.00263 atm An important concept of chemistry is significant figures. Since we are multiplying/dividing, we do not want any more significant figures than what the problem provided. 762 has 3 significant figures, so we will round the atmospheres to 1.00 atm. Now, let's plug it in to the ideal gas law. (1.00 atm)(14.2L)=n(0.08206 L atm/mol K)(298 K) Solving for our unknown, n (number of moles of Cl), we get that n=0.5807 mol Cl. Going back to the significant figures, usually constants do not count towards significant figures. So our final answer should be n=0.581 mol Cl.
Find the derivative of: y=x^2/3-3/x
The derivative of y will be dy/dx. This stands for the derivative of y (the function) with respect to x. The derivative of the first term in this equation is found by breaking it down to (1/3)*x^2. The derivative of x^2 is 2x because we multiply by the exponent, then decrease the exponent by 1. Therefore the derivative of the first term is (2/3)x. You can consider the x in the denominator of the second term to have a negative exponent. Another way to write this function would be y=x^2/3 -3*(x^-1). For the second term, we follow the same rules as the first. So we have -3*-1*(x^-2), or +3/(x^2). dy/dx=(2/3)x + 3/(x^2) is our answer.
Find the x and y values for the following system of equations: x+y=17 2x=y+2
For a system of equations, it is only solvable if the number of unknowns is equal to the number of equations. This system has two equations and two unknowns, so we will be able to solve it. There are two ways to solve: substitution and elimination. Today we will be using substitution, but elimination can be explained upon request. Substitution means solving for one variable in terms of the other and plugging it into the second equation. Let's rearrange the first equation. x+y=17 Subtract y from both sides. x=17-y Now, plug into the second equation. 2(17-y)=y+2 Multiply the 2 by both terms in parentheses to simplify. 34-2y=y+2 Solve for y. 32=3y y=32/3 Plug this into either equation to obtain the value for x. x+32/3=17 x+32/3=51/3 x=19/3